Learning Target 1: • I can identify that the

solution of an equation or inequality are the values that make the equation or inequality true.

Equations & ExpressionsSub Unit B

Solutions to

Equations &

Inequalities

What makes the sentence true?

x + 13 = 2925 – n = 12

9m > 18r ÷ 6 < 6

Learning Target #2: I can write expressions when solving a real-world or mathematical problem that contains one variable.

Learning Target #3: I can relate variables to a context.

My aunt is 32 years old, which is 18 years older than my sister. What is my sister’s age?• Choose a variable to

represent my sister’s age.• Write an equation to solve

the problem.

Writing Solution Sentences

Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68?

Choose a variable to represent the unknown.

Write an equation that will assist in solving the problem.

Solve the equation.

Write a solution statement.

m for $

$17 + m = $68

68 – 17 = 51

Jeanne needs $51 to buy the game.

1.) Roberto was given $5.00 for snacks at the beginning of a long day trip. At the first stop Roberto spent $2.38, at the second stop he spent $1.35. How much would that leave Roberto for the third stop, if t stands for the amount for the third stop?

2.) There are 268 total pieces of candy in a 1 pound bag. There are a total of four colors: red, yellow, green, and brown in the bag. The first three colors total 213 pieces. Show a solution sentence that shows how many pieces are brown, if B is the number of brown pieces.

3.) The largest pearl was found in 1934 in the shell of a giant oyster. It weighed 9 pounds 1 ounce. The largest diamond was found in 1905 and weighed 1 pound 4 ounces. If the pearls was placed on one side of a balance scale, and the diamond was placed on the other side of the balance scale, make a solution sentence to show how much weight will be needed on the side of the diamond in order to make the scale balance if w represents the weight needed.

4.)The worlds tallest man is 8 feet 11 inches tall. The worlds shortest man is 26 inches tall. If h represents the height, how much taller is the tallest man than the shortest man?

There’s a big carnival every year in our town. It’s opening tonight. It costs $5.00 to get in and $1.00 for every ride ticket you buy. Write an expression to represent the information.Determine how much it would cost to get into the carnival and buy 12 ride tickets.

The Carnival

MORE CARNIVAL QUESTIONS

Miguel is going to the carnival with his friend, Corey. Miguel is planning to buy 16 ride tickets. Write an equation to find the amount of money he’ll need to get in and buy ride tickets.

Corey has $27.00 to spend on admission and tickets. How many tickets will he be able to buy? Write an equation and use the letter x to stand for the number of tickets Corey will be able to puchase.

Miguel’s favorite ride is the Teacups. Some of the cups hold 2 people. Others hold 4 people. There are 9 cups in all, and when the ride is full, it holds 24 people. Draw a diagram that represents this information. Be prepared to explain your diagram.

Learning Target #4:I can apply the rules of solving one step equations using inverse operations.

Inverse operation: The

opposite operation that

will undo the current

operation.

INVERSE OPERATIONSaddition «» subtraction

multiplication «» division

SOLVING EQUATIONSby ADDING or SUBTRACTING

Whatever you do to one side of the equation….

you MUST do to the other!!!

7 + x = 10-7 -7 x = 3

b – 4 = 13 +4 +4 b = 17

GOAL: GET VARIABLE ALONE!

MUST SHOW YOUR WORK!

Solving Equations by Multiplying or Dividing

3x= 15 ÷3 ÷3 x = 5

b ÷ 4 = 9 ·4 ·4 b = 36

Learning Target #5: I can write an inequality in the form x>c or x<c to represent a constraint or condition in a real-world or mathematical problem.

WRITING INEQUALITIES FOR REAL-WORLD PROBLEMS

Inequalities

Match the Symbols

Less thanGreater than

Less than/Equal toGreater than/Equal to

< >≤≥

Important

Inequalities

Words

At least – greater than/equal toNo more than – less than/equal to

More than – greater thanLess than – less than

WARNINGMORE THAN & LESS THAN

have a DIFFERENT MEANING when ADDING & SUBTRACTING

compared to being used as an INEQUALITY!

BE CAREFUL

LESS THAN

• less than• below• fewer than

GREATER THAN

• more than• greater than• exceed• above

LESS THAN/EQUAL TO

• no more than• does not exceed• not above• at most• maximum

GREATER THAN/EQUAL TO

• no less than• at least• no fewer than• not under• minimum

Writing Inequalities from Statements

Examples:

1.) The temperature will not exceed 64 degrees.2.) Gabriella earned at least $75.00.3.) Jack needs to improve his marathon time by no more than 10 minutes.4.) Keith wants to buy a new car but cannot spend more than $3,500.5.) Each bus can hold at most 52 students.6.) DJ Joe can fit more than 120 CD’s in his travel case.

Learning Target #6: I can represent solutions to inequalities of the form x>c, x<c with infinitely many solutions on a number line diagram.

Solving Inequalities

7 + x > 10-7 -7 x > 3

b – 4 < 13 +4 +4 b < 17

b ÷ 4 > 9 ·4 ·4 b > 36

3x < 15 3 3 x < 5

Solve an Inequality like you solve an equation

Use the INVERSE OPERATION and keep the inequality.

Graphing Inequalities

x > 3*Draw a circle AT the number.*Shade the line in the direction the sign in pointing.>(Greater Than) Shade RIGHT<(Less Than) Shade LEFT

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

How does this relate to real life?

The average 1.5 inch match will burn for 45 seconds or less.

How can you represent this information using an inequality and graph?

37 38 39 40 41 42 43 44 45 46 47 48 49 50

Volunteer to Graph?

Volunteer to Write Inequality?

Other Real-Life Situations?

Weight Limits

Temperature

“Money”Interest RatesMedicine

Dosing Limits

Others???

Let’s Practice