1. Solve each inequality. Check your solution. 1. –3x ≥ 9 2.
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?
Course 2, Lesson 6-8

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

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

4. 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.
5 Use appropriate tools strategically.
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 two-step inequalities
Expressions and Equations
To solve two-step inequalities
Course 2, Lesson 6-8

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

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

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

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

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

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

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

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

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

16. Halfway through the bowling league season, Stewart has 34 strikes.
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.
The number of strikes plus two strikes per game is at
least 61. Let g represent the number of games he needs to bowl. 1 2
34 + 2g ≥ 61
Write the inequality.
– –34 3
Subtract 34 from each side. 4
2g ≥ 27
Simplify. 5
Divide each side by 2.
g ≥ 13.5 6
Simplify.
Stewart should have at least 61 strikes after 14 more games. 7
Need Another Example?

17. 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.
x ≥ 95, x ≥ 5.5. Tim will have at least $95 after mowing 6 more lawns.
Answer

18. 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 6-8

19. 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 answer:
To solve two-step inequalities by applying the properties of inequality
Course 2 Lesson 6-8

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