The document provides examples of solving two-step inequalities and writing and solving word problems as inequalities. It begins with six examples of solving two-step inequalities by combining like terms and then isolating the variable, including graphing the solution sets on number lines. The next examples involve writing and solving word problems as inequalities, such as writing an inequality to represent the number of magazine subscriptions needed to earn $35. The document concludes by reviewing the process of solving two-step inequalities.

1. Solve each inequality. Check your solution.
1. –3x ≥ 9
2.
3. 20k > 300
Solve each inequality. Graph the solution set on a number line.
4. 4p + 3 ≤ –1
5.
6. Javier earns $1.50 for every magazine subscription he sells. He needs
$35 to go on a trip with the travel club. Write an inequality to show the
number of subscriptions he needs to sell to achieve his goal?
15
2
y

4 7
2
n
 
Course 2, Lesson 6-8

2. Course 2, Lesson 6-8
ANSWERS
1. x ≤ –3
2. y < 30
3. k > 15
4. p ≤ –1
5. n > 6
6. 1.5x ≥ 35

3. WHAT does it mean to say
two quantities are equal?
Expressions and Equations
Course 2, Lesson 6-8

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 6-8 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.
5 Use appropriate tools strategically.
Course 2, Lesson 6-8 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 two-step inequalities
Course 2, Lesson 6-8
Expressions and Equations

7. Course 2, Lesson 6-8
Expressions and Equations
• two-step inequality

8. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
1. Solve 3x + 4 ≥ 16. Graph the solution set on a number line.
Write the inequality.
Graph the solution set.
Simplify.
3x + 4 ≥ 16
Subtract 4 from each side.
3x ≥ 12
– 4 – 4
Divide each side by 3.
Simplify.x ≥ 4
Draw a closed dot at 4 with an arrow to the right.

9. Answer
Need Another Example?
Solve 2x + 1 < 11. Graph the solution set on a
number line.
x < 5

10. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
2. Solve 5 + 4x < 33. Graph the solution set on a number line.
Write the inequality.
Graph the solution set.
Simplify.
5 + 4x < 33
Subtract 5 from each side.
4x < 28
– 5 – 5
Divide each side by 4.
Simplify.x < 7
Draw an open dot at 7 with an arrow to the left.

11. Answer
Need Another Example?
Solve 8 + 3x > 14. Graph the solution set on a
number line.
x > 2

12. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
3. Solve 7 – 2x > 11. Graph the solution set on a number line.
Write the inequality.
Graph the solution set.
Simplify.
7 – 2x > 11
Subtract 7 from each side.
You can check the solution by substituting a number less
than –2 into the original inequality. Try using –3.
Divide each side by –2. Reverse inequality symbol.
Write the inequality.Check 7 – 2x > 11
Draw an open dot at –2
with an arrow to the left.
x < –2 Simplify. Check your solution.
?
7 – 2(–3) > 11
13 > 11
Replace x with –3. Is the sentence true?
This is a true statement.
–7 –7
–2x > 4

13. Answer
Need Another Example?
Solve 6 – 3x ≤ 9. Graph the solution set on a
number line.

14. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
4. Solve – 5 < –8. Graph the solution set on a number line.
Write the inequality.
Graph the solution set.
x < –6 Simplify. Check your solution.
< – 3 Simplify.
– 5 < – 8
Add 5 to each side.
Multiply each side by 2.(2) < – 3(2)
Draw an open dot at –6 with an arrow to the left.
+ 5 + 5

15. Answer
Need Another Example?
Solve + 3 ≥ 7. Graph the solution set on a number
line.
x ≥ 16

16. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
5. Halfway through the bowling league season, Stewart has 34 strikes.
He averages 2 strikes per game. Write and solve an inequality to
find how many more games it will take for Stewart to have at least
61 strikes, the league record. Interpret the solution.
Write the inequality.
Stewart should have at least 61 strikes after 14 more games.
2g ≥ 27
Simplify.
34 + 2g ≥ 61
Subtract 34 from each side.
The number of strikes plus two strikes per game is at
least 61. Let g represent the number of games he needs to bowl.
–34 –34
Simplify.
Divide each side by 2.
7
g ≥ 13.5

17. Answer
Need Another Example?
Tim has already earned $40 mowing lawns. He
earns $10 per lawn. Write and solve an inequality
to determine how many more lawns he will have to
mow to have at least $95 for a new lawnmower.
Interpret the solution.
40 + 10x ≥ 95, x ≥ 5.5. Tim will have at least
$95 after mowing 6 more lawns.

18. How did what you learned
today help you answer the
WHAT does it mean to say
two quantities are equal?
Course 2 Lesson 6-8
Expressions and Equations

19. How did what you learned
today help you answer the
WHAT does it mean to say
two quantities are equal?
Course 2 Lesson 6-8
Expressions and Equations
Sample answer:
• To solve two-step inequalities by applying
the properties of inequality

20. Write about the similarities
and differences between
solving two-step equations
and two-step inequalities.
Ratios and Proportional RelationshipsExpressions and Equations
Course 2 Lesson 6-8