1. Solve each inequality. Graph the solution set on a number line.
1. x – 15 > 3
2. g + 3 ≤ –20
3. 11 ≥ t – 8
Solve each inequality. Graph the solution set on a number line.
4. 34 < 6 + d
5. 5 – f ≥ 10
6. Jonas has $75 to spend on new clothes. The pair of jeans he wants costs $ What is the most Jonas can spend on shirts?
Course 2, Lesson 6-7

2. ANSWERS 1. x > 18 2. g ≤ –23 3. t ≤ 19 4. d > 28; 5. f ≤ –5;
6. $26.50
Course 2, Lesson 6-7

3. two quantities are equal?
Expressions and Equations
WHAT does it mean to say
two quantities are equal?
Course 2, Lesson 6-7

4. Solve word problems leading to inequalities of the form px + q > r
Expressions and Equations
7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
7.EE.4b
Solve word problems leading to inequalities of the form px + q > r
or px + q < r, where p, q, and r are specific rational numbers. Graph
the solution set of the inequality and interpret it in the context of
the problem.
Course 2, Lesson Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

5. Mathematical Practices
Expressions and Equations
Mathematical Practices
1 Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure.
Course 2, Lesson Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

6. To solve inequalities when multiplying
Expressions and Equations
To solve inequalities when multiplying or dividing by a positive number
To solve inequalities when multiplying
or dividing by a negative number
Course 2, Lesson 6-7

7. Multiplication Property of Inequality Division Property of Inequality
Expressions and Equations
Multiplication Property of Inequality
Division Property of Inequality
Course 2, Lesson 6-7

8. Multiplication and Division Properties of Inequality, Positive Number
Expressions and Equations
Multiplication and Division Properties of Inequality,
Positive Number
Words The and the state that an inequality remains true when you multiply or divide each side of an inequality by a positive number.
Symbols For all numbers a, b, and c, where c > 0,
1. if a > b, then ac > bc and
2. if a < b, then ac < bc and
These properties are also true for a ≥ b and a ≤ b.
Multiplication Property of Inequality
Division Property of Inequality
Course 2, Lesson 6-7

9. The solution is x ≤ 5. You can check this solution by
Step-by-Step Example 1.
Solve 8x ≤ 40. 1
8x ≤ 40
Write the inequality. 2
Divide each side by 8. 3
x ≤ 5
Simplify. 4
The solution is x ≤ 5. You can check this solution by
substituting 5 or a number less than 5 into the inequality.
Need Another Example?

10. Need Another Example?
Solve 5x > 30.
x > 6
Answer

11. The solution is d > 14. You can check this solution by
Step-by-Step Example 2.
Solve > 7.
> 7 1
Write the inequality.
> 2(7) 2
Multiply each side by 2. 3
d > 14
Simplify. 4
The solution is d > 14. You can check this solution by
substituting a number greater than 14 into the inequality.
Need Another Example?

12. Need Another Example?
Solve 3 ≥ .
12 ≥ h or h ≤ 12
Answer

13. Multiplication and Division Properties of Inequality, Negative Number
Expressions and Equations
Multiplication and Division Properties of Inequality,
Negative Number
Words When you multiply or divide each side of an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true.
Symbols For all numbers a, b, and c, where c < 0,
1. if a > b, then ac < bc and
2. if a < b, then ac > bc and
Examples > 1 –4 < 16
–2(7) < –2(1) Reverse the symbols >
–14 < – > –4
These properties are also true for a ≥ b and a ≤ b.
Course 2, Lesson 6-7

14. Solve −2g < 10. Graph the solution set on a number line.
Step-by-Step Example 3.
Solve −2g < 10. Graph the solution set on a number line. 1
– 2g < 10
Write the inequality. 2
Divide each side by –2
and reverse the symbol. 3
g > –5
Simplify. 4
Need Another Example?

15. Solve –4x ≤ 4. Graph the solution set on a number line.
Need Another Example?
Solve –4x ≤ 4. Graph the solution set on a number line.
x ≥ –1
Answer

16. Solve ≤ 4. Graph the solution set on a number line.
Step-by-Step Example 4.
Solve ≤ 4. Graph the solution set on a number line.
≤ 4 1
Write the inequality. 2
Multiply each side by –3 and reverse the symbol. 3
x ≥ –12
Simplify. 4
Need Another Example?

17. Solve > – 5. Graph the solution set on a number line.
Need Another Example?
Solve > – 5. Graph the solution set on a number line.
x < 20
Answer

18. Ling earns $8 per hour working at the zoo. Write and solve an
Step-by-Step Example 5.
Ling earns $8 per hour working at the zoo. Write and solve an
inequality that can be used to find how many hours she must
work in a week to earn at least $120. Interpret the solution. 1
Word
Amount earned times number is at amount earned
per hour of hours least each week.
Variable
Let x represent the number of hours.
Inequality
x ≥
8x ≥ 120 2
Write the inequality. 3
Divide each side by 8. 4
x ≥ 15
Simplify.
So, Ling must work at least 15 hours. 5
Need Another Example?

19. A plate weighs pound. A shelf can hold at most 20
Need Another Example?
A plate weighs pound. A shelf can hold at most 20
pounds. Write and solve an inequality to find how
many plates the shelf can hold. Interpret the solution.
x ≤ 20; x ≤ 80; The shelf can hold at most 80 plates.
Answer

20. How did what you learned today help you answer the
Expressions and Equations
How did what you learned
today help you answer the
WHAT does it mean to say
two quantities are equal?
Course 2 Lesson 6-7

21. How did what you learned today help you answer the
Expressions and Equations
How did what you learned
today help you answer the
WHAT does it mean to say
two quantities are equal?
Sample answers:
To keep the same inequality sign when multiplying or dividing each side of an inequality by a positive number
To reverse the inequality sign when multiplying or dividing each side of an inequality by a negative number
Course 2 Lesson 6-7

22. Expressions and Equations
Ratios and Proportional Relationships
How did the previous lesson on solving inequalities by adding or subtracting help you with today’s lesson?
Course 2 Lesson 6-7