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Unit 2 Inequalities 2.1 Graphing and Writing Inequalities 2.2 Solving by Adding and Subtracting 2.3 Solving by Multiplying and Dividing 2.4 Solving TwoStep and MultiStep Inequalities 2.5 Solving Inequalities with Variables on Both Sides 2.6 Solving Compound Inequalities 2.7 Solving Absolute Value Inequalities 2.1 Graphing and Writing Inequalities Standards: A.REI.3 Objectives: Students will be able to
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● Essential Question: Do Now:
Vocabulary:
Term Definition Example
Inequality
Solution of an inequality
Identifying Solutions of Inequalities Example 1) Describe the solutions of 3+x<9 in words. Let’s test values of x to see when the inequality will be true
x
3+x
3+x<9
Solution?
______________________________________________________________________________________________________________________________________________________________. Example 2) Describe the solution of 2p<8 in words. Graphing Inequalities
*A closed circle means _______________________________________. *An open circle means ________________________________________. Example 1) Graph − b > 3
Example 2) Graph x ≤ 4
Example 3) Graph − y ≥ 4 + 5
Example 4) Graph (3 )a > 2
1 − 1
Writing an Inequality from a Graph Write an inequality shown by the graph Example 1)
Example 2)
Example 3)
Example 4)
Exit Ticket
2.2 Solving Inequalities By Adding or Subtracting
Standards: A.REI.3 Objectives: Students will be able to
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● Essential Question: Do Now:
Let’s test this….
Using Addition and Subtraction to Solve Inequalities Solve each inequality and graph the solutions. Example 1) 6 x + 9 < 1
Example 2) x − 5 ≥ 3
Example 3) − − 4 + a ≤ 2
Example 4) − 0 − 3 + y < 1
Example 5) .3 .6 x + 4 ≥ 5
Real World Applications Example 1)
Example 2)
Exit Ticket
2.3 Solving Inequalities by Multiplying or Dividing
Standards: A.CED.1, A.REI.3 Objectives: Students will be able to
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● Essential Question: Do Now:
Let’s test this out…
Multiplying or Dividing by a Positive number Just like solving inequalities using addition and subtraction, solving ______________________________________________________________________________________________________________________ is the same thing as solving equations. Solve the inequalities and graph the solutions. Example 1) x − 6 4 > 1
Example 2) −5
x ≤ 1
Example 3) −2
y < 3
Example 4) 9.5x4 ≥
Multiplying or Dividing by a Negative Number What happens when we multiply or divide both sides of an inequality by a negative number?
Solve each inequality and graph the solutions. Example 1) x 4 − 7 > 1
Example 2) −x
−3 < 3
Example 3) .1x .3− 3 ≤ 9
Example 4) −6
−x ≥ 1
Exit Ticket
2.4 Solving TwoStep and MultiStep Inequalities
Standards: A.CED.1, A.REI.3 Objectives: Students will be able to
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● Essential Question: Do Now:
Solving TwoStep and MultiStep inequalities is just like solving twostep and multistep equations, but remember that when you multiply or divide by a ______________________________, you must __________________________________________________________. Solving MultiStep Inequalities Solve the inequality and graph the solutions. Example 1) v − 3 − 8 + 9 > 5
Example 2) −− 8 ≥ v − 3
Example 3) −4
6+n > 2
Example 4) − − 5 + 8
k ≤ 7
Simplifying before Solving Inequalities Solve each inequality and graph the solutions. Example 1) 0 (b ) − 9 > 6 − 6
Example 2) (r ) − 0 4 − 7 ≥ 2
Example 3) 06 − (5n )2 > 4 + 5 + 7
Example 4) −b − 3
5 + 41 < 5
12
Exit Ticket
2.5 Solving Inequalities with Variables on Both Sides
Standards: A.CED.1, A.REI.1, A.REI.3 Objectives: Students will be able to
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● Essential Question: Do Now:
Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. Example 1) 6 r− 1 − 7 < r
Example 2) v − v− 4 + 8 > 8
Example 3) n 0 − 3 − 1 ≤ n + 6
Example 4) v v 61 − 2 < 3 + 1
Simplifying Each Side Before Solving Solve each inequality and graph the solutions. Example 1) (2 a) 6 a 8 + 6 ≥ 1 − 6
Example 2) (a ) − a 4− 4 − 7 > 4 + 3
Example 3) x (3 x)6 < 6 + 4
Example 4) 0 b − (5b )− 3 − 8 ≤ 6 − 6
All Real Numbers as Solutions or No Solutions *Some inequalities are true no matter what value is substituted for the variable. For these inequalities, the solution is _____________________. *Some inequalities are false no matter what value is substituted for the variable. For these inequalities, there ____________________________. Solve each inequality. Example 1) x + 5 ≥ x + 3
Example 2) (x ) x 2 + 3 < 5 + 2 Exit Ticket
1.6 Solving Compound Inequalities Standards: A.REI.3 Objectives: Students will be able to
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● Essential Question: Do Now:
Vocabulary:
Term Definition Example
Compound Inequality
Intersection
Union
Solving Compound Inequalities Involving AND Example: We want to graph the solutions of x<10 and x>0. First draw a venn diagram to see some solutions. Then graph the solutions to both inequalities. The intersection of the graph shows the numbers that are ___________________________________________.
Solve each inequality and graph the solutions. Example 1) 4 ≤ x + 2 ≤ 8
Example 2) x− 2 ≤ 2 + 3 ≤ 9
Example 3) n 1− 4 ≤ 3 + 5 < 1
Solving Compound Inequalities Involving OR We want to find the solutions for the inequalities x>10 or x<0. First draw a Venn diagram to see the solutions of each inequality. Then graph the solutions of each inequality. The union will show the solutions of __________________________________________________________.
Example 1) or −− 4 + a > 1 − 4 + a < 3
Example 2) x or 3x 22 ≤ 6 > 1
Example 3) x 1 or 2x −7 > 2 < 2
Writing a Compound Inequality from a Graph Example 1)
Does this inequality involve AND or OR? Are there open or closed circles? Example 2)
Does this inequality involve AND or OR? Are there open or closed circles? Exit Ticket
1.7 Solving Absolute Value Inequalities
Standards: A.CED.1, A.REI.3 Objectives: Students will be able to
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● Essential Question: Do Now:
Solving Absolute Value Inequalities Involving <
Solve each inequality and graph the solutions Example 1) 2 x| | + 3 < 1
Example 2) || 7
n || < 5
Example 3) 6 − b| 4 | ≤ 3
Example 4) 05 6n| | ≤ 6
Solving Absolute Value Inequalities Involving >
Example 1) a| + 7| ≥ 1
Example 2) k| − 2| − 2 > 9
Example 3) || 4
p || > 3
Example 4) 0− x| 2 | + 4 ≥ 2
Special Cases of AbsoluteValue Inequalities *If you get a statement that is true for all values of a variable, ____________________ are solutions of the original inequality. *If you get a false statement when solving an absolutevalue inequality, the original inequality ________________________________________> Example 1) − 1x| | − 9 ≥ 1
Example 2) −4 x .5| − 3 | ≤ 8 Exit Ticket
Points for Unit 2 2.1 Graphing and Writing Inequalities
/5 2.2 Solving by Adding and Subtracting
/5 2.3 Solving by Multiplying and Dividing
/5 2.4 Solving TwoStep and MultiStep Inequalities /5
2.5 Solving Inequalities with Variables on Both Sides /5 2.6 Solving Compound Inequalities /5 2.7 Solving Absolute Value Inequalities
/5 Total /35