lesson 20: one- and two-step inequalities [objectiventnmath.kemsmath.com/level g teacher notes/grade...

Mathematics Success – Grade 7 T483

LESSON 20: One- and Two-Step Inequalities

[OBJECTIVE]The student will solve and graph the solutions to one-step and two-step inequalities in mathematical and real-world situations.

[PREREQUISITE SKILLS]One-step and two-step equations, integer operations, order of operations, number line

[MATERIALS]Student pages S246–S263

[ESSENTIAL QUESTIONS]1. How does the solution of the inequality x + 6 < 10 differ from the solution of the

equation x + 6 = 10?2. When do you use an open circle when graphing an inequality? a closed circle?3. How do you make an inequality a true statement when multiplying or dividing by

a negative number? Explain your answer.

[WORDS FOR WORD WALL]inequality, inverse operation(s), isolate the variable, less than, greater than, less than or equal to, greater than or equal to, inequality symbols (<, >, ≤, ≥), solution, number line

[GROUPING]Cooperative Pairs (CP), Whole Group (WG), Individual (I)

[LEVELS OF TEACHER SUPPORT]Modeling (M), Guided Practice (GP), Independent Practice (IP)

[MULTIPLE REPRESENTATIONS]SOLVE, Algebraic Formula, Pictorial Representation, Verbal Description, Graphic Organizer, Graph

[WARM-UP] (IP, WG, I) S246 (Answers on T500.)• Have students turn to S246 in their books to begin the Warm-Up. Students will

solve one-step and two-step equations. Monitor students to see if any of them need help during the Warm-Up. Have students complete the problems and then review the answers as a class. {Verbal Description, Algebraic Formula}

[HOMEWORK]Take time to go over the homework from the previous night.

[LESSON] [3 – 4 Days (1 day = 80 minutes) – M, GP, WG, CP, IP]

Mathematics Success – Grade 7T484

SOLVE Problem (GP, WG) S247 (Answers on T501.)

Have students turn to S247 in their books. The first problem is a SOLVE problem. You are only going to complete the S step with students at this point. Tell students that during the lesson they will learn how to solve one-step inequalities. They will use this knowledge to complete the SOLVE problem in this section of the lesson. {SOLVE, Verbal Description, Graphic Organizer}

Inequality Symbols (M, GP, CP, WG) S247 (Answers on T501.)

WG, M, GP, CP Students will use the following activity to review comparing integers and the four inequality symbols (<, >, ≤, ≥) less than, greater than, less than or equal to, greater than or equal to. Assign the roles of Partner A and Partner B to students. {Pictorial Representation, Verbal Description, Graphic Organizer, Algebraic Formula}


MODELING

Inequality Symbols

Step 1: Have students look at the number line on the bottom of S247. • Have students identify the location of zero on the number line. • Partner A, what type of integers are to the right of zero on the number

line? (positive integers) • Partner B, what type of integers are to the left of zero on the number

line? (negative integers)

Step 2: Partner A, is 6 greater than or less than zero? (6 is greater than zero because it is to the right of zero on the number line.)

• Partner B, is negative 8 greater than or less than zero? (Negative 8 is less than zero because it is to the left of zero on the number line.)

Step 3: Have students look at Problem 1. • Partner A, identify the two values we are comparing. (2 and 5) • Partner B, what sign can we use between the two values to make a

true statement? (less than symbol, <) Record the symbol. • Partner A, how can we write the relationship using words? (Two is less

than five.) Record. • Have students pairs complete Problems 2 – 4 and then review the

answers as a class.



One-Step Inequalities – Addition and Subtraction (M, GP, IP, CP, WG) S248 (Answers on T502.)

WG, M, GP, CP Students will explore the relationship between addition and subtraction equations and inequalities. They will also solve one-step addition and subtraction inequalities. Be sure students know their designation as Partner A or Partner B. {Pictorial Representation, Verbal Description, Graphic Organizer, Algebraic Formula}

MODELING

One-Step Inequalities – Addition and Subtraction

Step 1: Have students complete the equations for Problems 1 – 4 in the Equation column on S248. Review the answers as a whole group. • Partner A, what is the meaning of an equation and its equal sign?

(The equal sign means that the values on both sides of the equation must be the same. The equation must be a true statement.)

Step 2: Have students look at the problem in the Inequality column, x + 2 < 4.• Partner B, how is this problem different from the problem in Column

1? (It has an inequality symbol instead of an equals sign.) • What does the inequality symbol mean? (The value on one side of the

symbol is less than, less than or equal to, greater than, or greater than or equal to the value on the other side of the symbol.)

• Explain to students that inequalities can be solved using the same process as the one used to solve equations and that like an equation, an inequality must be a true statement.

• Have students identify the two things that they need to remember when they are solving an equation. (isolate the variable and balance the equation)

• Tell students that in solving inequalities they will also need to isolate the variable and that whatever they do to one side of the inequality they must also do to the other.

Step 3: Have student pairs discuss how they found the solution for the equation in Problem 1. (They had to isolate the variable by using the inverse operation and subtracting 2 from both sides.)• Partner A, what was the solution for this equation? (x = 2)• Have student pairs discuss how they can apply what they know about

solving equations to complete the first step in solving the inequality in Problem 1. (They can isolate the variable by subtracting 2.)

• Ask students what they will need to do to the other side of the inequality. (also subtract 2) Model for students how to subtract 2 from both sides of the inequality as they work on S248.



Step 4: Partner B, what is the value of x in the inequality? (x < 2) x + 2 < 4 –2 –2 x < 2

Step 5: Have student pairs discuss how they checked the equation. (We substituted the value for x back in the original equation.)• Tell students that they can check the answer for an inequality using

the same process as the one they used to check the answer for an equation.

• Have students look back at the equation in Problem 1.• Partner A, how many values were there for the variable x? (1)• In an inequality, there is more than one value that will make the

statement true. Have students look at the inequality they just solved. • Partner B, what is the solution for the inequality in Problem 1? (x < 2) • Partner A, what does this solution mean? (Any value that is less than

2 should work when substituted back into the original inequality.)

Step 6: Under the “Check” for the Problem 1 inequality, what values can we use to check the inequality? (any value that is less than two)• Model for students how to substitute the value of 1 back into

the original inequality. Have students complete the check on S248 as you model. Explain that the value of 1, which is less than 2, makes this a true statement because 3 is less than 4.

x + 2 < 4 1 + 2 < 4 3 < 4 True

Step 7: Choose a value that is greater than 2 such as 5 to try in the original inequality. Explain that any value greater than 2 will make the inequality not true.

x + 2 < 4 5 + 2 < 4 7 < 4 Not a true statement because 7 is not less than 4

IP, CP, WG Have students work in partners to complete the inequalities for Problems 2–4 on S248. Remind students to check each inequality after solving. (Suggested values are given for the check.) Have students come back together as a class and share their results. {Verbal Description, Graphic Organizer, Algebraic Formula}



One-Step Inequalities – Multiplication and Division (M, GP, IP, CP, WG) S249 (Answers on T503.)

WG, M, GP, CP Students will explore the relationship between multiplication and division equations and inequalities. They will also solve one-step multiplication and division inequalities. Be sure students know their designation as Partner A or Partner B. {Pictorial Representation, Verbal Description, Graphic Organizer, Algebraic Formula}

MODELING

One-Step Inequalities – Multiplication and Division

Step 1: Have students complete the equations for Problems 1 – 4 in the Equation column on S249. Review the answers as a whole group.

• Partner A, what is the meaning of an equation and its equal sign? (The equal sign means that the values on both sides of the equation must be the same. The equation must be a true statement.)

Step 2: Have students look at the problem in the Inequality column, which is 2x < 4.

• Partner B, how is this problem different from the problem in Column 1? (It has an inequality symbol instead of an equals sign.)

• What does the inequality symbol mean? (The value on one side of the symbol is less than, less than or equal to, greater than, or greater than or equal to the value on the other side of the symbol.)

• Have students identify the two things that they need to remember when they are solving an equation. (isolate the variable and balance the equation)

• Tell students that in solving inequalities they will also need to isolate the variable and that whatever they do to one side of the inequality they must also do to the other.

Step 3: Have student pairs discuss how they found the solution for the equation in Problem 1. (They had to isolate the variable by dividing both sides by 2.)

• Partner A, what was the solution for this equation? (x = 2) • Have student pairs discuss how they can apply what they know about

solving equations to complete the first step in solving the inequality in Problem 1. (They can isolate the variable by dividing by 2).

• Ask students what they will need to do to the other side of the inequality. (also divide by 2) Model for students how to divide by 2 on both sides of the inequality as they work on S249.



Step 4: Ask students what the value of x is in the inequality. (x < 2) 2x < 4 2 2 x < 2

Step 5: Have student pairs discuss how they checked the equation. (We substituted the value for x back in the original equation.)

• Tell students that they can check the answer for an inequality using the same process as the one they used to check the answer for an equation.

• Have students look back at the equation in Problem 1. • Partner A, how many values were there for the variable x? (1) • In an inequality, there is more than one value that will make the

statement true. Have students look at the inequality they just solved.

• Partner B, what is the solution for the inequality in Problem 1? (x < 2) • Partner A, what does this solution mean? (Any value that is less than

2 should work when substituted back into the original inequality.)

Step 6: Under the “Check” for the Problem 1 inequality, what values can we use to check the inequality? (any value that is less than two)

• Model for students how to substitute the value of 1 back into the original inequality. Have students complete the check on S249 as you model. Explain that the value of 1, which is less than 2, makes this a true statement because 2 is less than 4.

2(1) < 4 2 < 4 True


2(5) < 4 10 < 4 Not a true statement because 10 is not less than 4

IP, CP, WG: Have students work in partners to complete the inequalities for Problems 2–4 on S249. Remind students to check each inequality after solving. (Suggested values are given for the check.) Have students come back together as a class and share their results. {Verbal Description, Graphic Organizer, Algebraic Formula}



MODELING

Graphing Inequalities

Step 1: Have students look at the inequality in Problem 1 and identify the solution. (x < 2). Have them write the solution in the third column on S248 as you model.

Step 2: Because there is more than one value that can be a solution to the inequality, the solution can be graphed using a number line.

Step 3: We can use the solution of the inequality (x < 2) to determine how to number the number line and how to graph the solution.

• Explain that because the solution contains a positive 2, students can place a 2 in the middle of the number line and label values to the left and right of the 2.

0 1 2 3 4

Step 4: Partner A, is the value of 2 a solution for the inequality? Explain your thinking. (No, because x is less than 2.)

• Model for students how to begin graphing the inequality by drawing a circle above the 2. Tell students that the circle above the 2 is open because 2 is not included in the solution.

Step 5: Have student pairs discuss which direction the arrow should extend. • Partner B, which direction should the arrow point? Justify your answer.

(The arrow should start at the two and point to the left because all the solutions are values less than positive 2.)

• Partner A, what does the arrowhead at the end of the ray indicate? (The values for the solution will continue to infinity.)

Step 6: Have students look at the inequality in Problem 2. Ask them what the solution was for the inequality (x ≥ -6). Have them write the solution in the third column on S248.

Graph Inequalities (M, GP, IP, CP, WG) S248, S249 (Answers on T502, T503.)

WG, M, GP, CP Students will graph the solution for one step inequalities. Be sure students know their designation as Partner A or Partner B. {Pictorial Representation, Verbal Description, Graphic Organizer, Algebraic Formula}



Step 7: We can use the solution of the inequality (x ≥ -6) to determine how to number the number line and how to graph the solution.

• Explain that because the solution contains a negative 6, students can place the negative 6 in the middle of the number line and label values to the left and right of the negative 6.

-8 -7 -6 -5 -4

Step 8: Model for students how to begin graphing the inequality by drawing a circle above the -6.

• Partner A, is -6 a solution to the inequality? (Yes, because x is greater than or equal to negative 6.)

• Explain that the circle above the -6 is solid because -6 is included in the solution.

Step 9: Have student pairs discuss which direction the arrow should extend. • Partner B, which direction should the arrow point? Justify your answer.

(The arrow should start at the negative six and point to the right because all the solutions are values that are equal to or greater than negative six.)

• Partner A, what does the arrowhead at the end of the ray indicate? (The values for the solution will continue to infinity.)

IP, CP, WG: Have students work in partners to complete the graphs for the inequalities for Problems 3 and 4 on S248 and Problems 1–4 on S249. Have students come back together as a class and share their results. {Graphic Organizer, Algebraic Formula, Pictorial Representation}

Inequalities with Negative Numbers (M, GP, IP, CP, WG) S250 (Answers on T504.)

WG, M, GP, CP Students will explore the relationship with inequalities and negative numbers. This will build the foundation for solving inequalities that use multiplication and division of negative integers. Be sure students know their designation as Partner A or Partner B. {Pictorial Representation, Verbal Description, Graphic Organizer, Algebraic Formula}



MODELING

Inequalities with Negative Numbers

Step 1: Have students look at Problem 1. • Partner A, is the number statement true or false? Explain your answer.

(The statement is true.) Record. (4 is less than 7) • Have students look at Column 3. • Partner A, when we were solving equations and inequalities and we

used multiplication or division, what did we have to do? (Whatever operation we used on one side of the equals sign or inequality sign, we had to do to the other.)

Step 2: Partner B, what value are we multiplying by in Problem 1? (negative 2) • Partner A, what is the product on the left side of the inequality?

(negative 8) • Partner B, what is the product on the right side of the inequality

(negative fourteen) • Ask students if the statement -8 < -14 is true or false. (false) • Partner A, what do we know about two numbers written with an

inequality sign? (It must be a true statement.) • Have student pairs discuss what strategies they can use to make the

statement true. (We can flip the inequality sign.) Record. • Partner A, how can we read the inequality after we flip the inequality

sign? (Negative eight is greater than negative fourteen or -8 > -14.) Record.

Step 3: Partner B, what value are we dividing by in Problem 2? (negative 3) • Partner A, what is the quotient on the left side of the inequality?

(negative 4) • Partner B, what is the quotient on the right side of the inequality?

(negative 1) • Ask students if the statement -4 > -1 is true or false. (false) • Partner A, what do we know about two numbers written with an

inequality sign? (It must be a true statement.) • Have student pairs discuss what strategies they can use to make the

statement true. (We can flip the inequality sign.) Record. • Partner A, how can we read the inequality after we flip the inequality

sign? (Negative 4 is less than negative one or -4 < -1.) Record.

Step 4: Model the same procedure for Problems 3 and 4. Fill in the blanks with students to complete the statement at the bottom of S250.

• When solving inequalities, you must (switch) the inequality symbol when you (multiply) or (divide) by a (negative) value.



Inequalities – Multiply and Divide with Negative Numbers (M, GP, IP, CP, WG) S251 (Answers on T505.)

M, WG, GP, CP: Have students turn to S251 in their books. Use the following activity to help students solve and graph inequalities that include negative numbers with multiplication and division. Be sure partners know their designation as Partner A or Partner B, {Pictorial Representation, Verbal Description, Graphic Organizer, Algebraic Formula}

MODELING

Inequalities – Multiply and Divide with Negative Numbers

Step 1: Have students look at Problem 1. • Partner A, what do we need to do to isolate the variable? (Divide both

sides by negative 2.) • Partner B, on page S250 when we were dividing or multiplying by a

negative value, what did we have to do to make the inequality true? (We need to flip the inequality sign to make the inequality true.)

-2x-2

> 4-2

x < -2

Step 2: In the second column, model how to check the answer by substituting in a solution into the original inequality.

• Have student pairs discuss the question, “What did you do?” (Since we have to divide by a negative to solve the inequality we flip the symbol to less than to make the inequality true.) Record.

Step 3: In the third column, write the solution to the inequality and then model for students how to graph the solution on the number line. Review with students how to set up the number line using the solution as the middle value on the number line.

Step 4: Have students look at Problem 3. Ask students what they need to do to isolate the variable. (Multiply both sides by negative 2.)

• Partner A, when we multiply by a negative value, what do we need to do to the inequality symbol? (Flip it to the opposite symbol.)

(-2) x-2 < 2 (-2)

x > -4



Step 5: In the second column, model how to check the answer by substituting in a solution into the original inequality.

• Have student pairs discuss and then explain what they did during the process of solving the inequality. (Since we had to multiply by a negative to solve the inequality, we flipped the symbol to make the inequality true.) Record.

Step 6: In the third column, write the solution to the inequality and then model for students how to graph the solution on the number line. Review with students how to set up the number line using the solution as the middle value on the number line.

IP, CP, WG: Have students work in partners to solve and graph the inequalities for Problems 2 and 4 on S251. Remind students that because they are dividing or multiplying by a negative number, they will have to flip the inequality symbol at the end to make the inequality true. Have students come back together as a class and share their results. {Graphic Organizer, Algebraic Formula, Pictorial Representation}

Solve and Graph One-Step Inequalities (IP, CP, WG) S252, S253 (Answers on T506, T507.)

IP, CP, WG: Have students work in partners to solve and graph the inequalities for Problems 1–8 on S252 and S253. Remind students that when they are dividing or multiplying by a negative number, they will have to flip the inequality symbol at the end to make the inequality true. Have students come back together as a class and share their results. {Graphic Organizer, Algebraic Formula,

Pictorial Representation}


Have students turn to S254 in their books. Remind students that the SOLVE problem is the same one from the beginning of the lesson. Complete the SOLVE problem with your students. Ask them for possible connections from the SOLVE problem to the lesson. (They will write and solve a one-step multiplication inequality.) {SOLVE, Verbal Description, Algebraic Formula, Graphic Organizer}


MODELING

Two-Step Inequalities

Step 1: Have students look at Problem 1 on S255. • Partner A, identify the equation. (It is a two-step equation.) • Partner B, explain the meaning of a two-step equation. (It is an

equation that involves two operations to solve for the solution.) • Have students discuss what the steps were when solving two-step

equations. [When solving two-step equations we follow the order of operations (PEMDAS) in reverse order. Usually, multiplication and division are completed before addition and subtraction. However, in two-step equations, students will add or subtract before multiplying or dividing because we work toward isolating the operation with the variable.]

Step 2: Have student pairs solve the two-step equation for Problem 1 and then check the solution. Review the problem as a whole group.

Step 3: Have students look at the problem in the second column which is 2x − 3 < 7.

• Partner A, how is this problem different from the equation? (It has an inequality symbol instead of an equals sign.)

• Partner B, how is solving an inequality similar to solving an equation? (We can follow the same steps: we isolate the variable and whatever operation we apply to one side of the inequality, we must apply to the other.)



Have students turn to S255 in their books The first problem is a SOLVE problem. You are only going to complete the S step with students at this point. Tell students that during this section of the lesson they will learn how to solve two-step inequalities in mathematical and real-world situations. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE, Verbal Description, Graphic Organizer}

Two-Step Inequalities (M, GP, CP, IP, WG) S255, S256, S257

(Answers on T509, T510, T511.)

M, WG, GP, CP: Have students turn to S255 in their books. Use the following activity to help students solve and graph the solution set for two-step inequalities. Be sure partners know their designation as Partner A or Partner B, {Pictorial Representation, Verbal Description, Graphic Organizer, Algebraic Formula}



Step 4: Have student pairs discuss the first step in solving the inequality. (The first step is to add a three to both sides.)

• Model how to add 3 to both sides as students do the same. • Partner A, is my variable isolated? (No) What operation do we do to

isolate the variable? (The coefficient is multiplied by the variable, so we use the inverse operation of division.)

• Model how to divide both sides by 2 as students do the same. • Partner A, is my variable now isolated? (Yes) • Partner B, have I performed the same operations on both sides of the

inequality? (Yes) • What is the solution for the inequality? (x < 5) 2x – 3 < 7 +3 +3

2x2

< 102

x < 5

Step 5: Have students discuss how they checked the solution for a one-step inequality. (They chose a value that would be part of the solution set and substituted it back into the original inequality and solved to see if it was a true statement.)

• Partner A, what is the suggested value to try in the Check? (1) • Partner B, is 1 less than the solution of x < 5? (Yes) What does this

mean? (It means that if we substitute the value of 1 in for x in the inequality, the answer should be a true inequality.)

Step 6: Model for students how to substitute the value of 1 back into the original inequality. Have students complete the check on S255 as you model.

• The value of 1, which is less than 5, makes this a true statement because -1 is less than 7.

2(1) – 3 < 7 2 – 3 < 7 -1 < 7 True


2(7) – 3 < 7 14 – 3 < 7 11 < 7 Not a true statement because 11 is not less than 7

Step 8: Have students look at the number line in the third column. • What is the solution for the inequality? (x < 5) Have them write the

solution in the third column on S255.



Step 9: Have students discuss how they modeled the solution to a one-step inequality. Share answers as a whole group. (Use the value from the solution as the middle number on the number line scale. Draw a circle at the value given.)

3 4 5 6 7

Step 10: Model for students how to begin graphing the inequality by drawing a circle above the 5 as they work on S255.

• Partner A, is 5 a solution to the inequality? (No, because x is less than 5.)

• Partner B, how do we model on the number line that 5 is not part of the solution set? (We have an empty circle.)

• Partner A, how do we know which direction the arrow should point for the graph? (We need to extend the arrow from the 5 to the left because we want values that are less than 5.)

• Partner B, what does the arrowhead mean? (The arrowhead at the end of the line shows that the values for the solution will continue to infinity.)

3 4 5 6 7

Step 11: Use the steps above to model solving the equation and inequality for Problem 2.

IP, CP, WG: Have students work in partners to complete Problems 1 – 8 on pages S256 and S257. Students should solve each inequality, check its solution, and then graph the solution on the number line in the third column. {Verbal Description, Pictorial Representation, Algebraic Formula, Graphic Organizer}

Two-Step Inequalities – Multiplication and Division with Negative Numbers (M, WG, IP, GP, CP) S258, S259 (Answers on T512, T513.)

M, WG, GP, CP: Have students turn to S258 in their books. Use the following activity to help students explore solving and graphing the solution set for two-step inequalities with negative integers. Be sure partners know their designation as Partner A or Partner B. {Pictorial Representation, Verbal Description, Graphic Organizer, Algebraic Formula}



MODELING

Two-Step Inequalities – Multiplication and Division with Negative Numbers

Step 1: Have student pairs work through the exploration activity for Problems 1 and 2 on the top of S258. Students can refer back to S250 as needed.

Review the answers as a whole group and fill in the blanks below the graphic organizer.

Step 2: Have students look at Problem 3. • Partner A, what is the first step in solving this inequality? (Add 4 to

both sides.) • Partner B, have we isolated our variable? (No) • Partner A, what is our next step? (We need to divide both sides of the

inequality by a negative 2.) • Have student pairs discuss what we need to do when dividing by a

negative integer in order to make the inequality a true statement. (We need to flip the inequality sign to make the inequality true.)

• Model how to divide both sides of the inequality by -2.

-2x – 4 ≤ 16 +4 +4

-2x-2

≤ 20-2

x ≥ -10

Step 3: Have students look at the second column: Check. • Partner A, what is the suggested value to try? (4) • Partner B, why would this be a good value to try to prove the inequality?

(Because it is greater than or equal to negative 10.) • Have students substitute in the 4 for the variable and complete the

check. • Partner A, did the value of 4 prove the inequality had the correct

solution set? (Yes) Explain why. (When we substituted in the value of 4 we had a true inequality. Negative 12 is less than 16.)

-2(4) – 4 ≤ 16 -8 – 4 ≤ 16 -12 ≤ 16

Step 4: In the third column, write the solution to the inequality. Have students work with a partner to graph the solution and then share

the solution as a whole group. Students should be prepared to explain and justify their graph. If students need support in graphing the solution, have them refer back to page S257.

Step 5: Model Problem 4 on S258 using the same questioning strategies as with Problem 3. (Use Steps 2 – 4)



IP, CP, WG: Have students work in partners to complete Problems 1 – 4 on pages S259. Students should solve each inequality, check its solution, and then graph the solution on the number line in the third column. {Verbal Description, Pictorial Representation, Algebraic Formula, Graphic Organizer}

Writing and Solving Inequalities in Real-World Situations (M, GP, WG, CP, IP) S260 (Answers on T514.)

WG, M, GP, CP Students will write and solve two-step division equations with integers that represent real-world situations. Be sure students know their designation as Partner A or Partner B. {Verbal Description, Graphic Organizer, Algebraic Formula}

MODELING

Writing and Solving Two-Step Inequalities in Real-World Situations

Step 1: Have students look at Problem 1 on S260. • Have students read the word problem. • Partner A, what variable will we use to represent the hours in the

word problem? (h) • Partner B, what is on the left side of the inequality? (the amount she

started with) • Partner A, what other information will be written on the left side of the

inequality? (the variable times the charge per hour) • Partner B, what will be written on the right side of the inequality? (the

total in her account) • Have students write the equation in Column 2. (10h + 50 ≥ 305)

Step 2: Partner A, what two operations are represented in Problem 1? (multiplication and addition)

• Partner B, what operations will we use to solve the problem? (subtraction and division)

• Have student pairs work together to solve the problem in the third column.

• Review the solution to the equation. (h ≥ 25.5 hours) • Have students check the solution to the inequality.

lesson 20: one- and two-step inequalities [objectiventnmath.kemsmath.com/level g teacher notes/grade...

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