(7) Lesson 6.7

1. Solve each inequality.
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 $48.50. 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. WHAT does it mean to say
two quantities are equal?
Expressions and Equations
Course 2, Lesson 6-7

4. • 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 6-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

5. Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 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 6-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

6. • 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
Expressions and Equations

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

8. Course 2, Lesson 6-7
Expressions and Equations
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
.
a b
c c

.
a b
c c


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

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

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

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

13. Course 2, Lesson 6-7
Expressions and Equations
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 7 > 1 –4 < 16
–2(7) < –2(1) Reverse the symbols >
–14 < –2 1 > –4
These properties are also true for a ≥ b and a ≤ b.
.
a b
c c

.
a b
c c

4
4

16
4

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

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

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

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

18. 1
Need Another Example?
2
3
4
5
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.
Write the inequality.
Simplify.
8x ≥ 120
Divide each side by 8.
x ≥ 15
Word
Variable
Inequality
Amount earned times number is at amount earned
per hour of hours least each week.
Let x represent the number of hours.
8 x ≥ 120
So, Ling must work at least 15 hours.

19. Answer
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.

20. 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
Expressions and Equations

21. 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
Expressions and Equations
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

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