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
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.
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.
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
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
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