1. Solving Two-Step Inequalities
12-7
Solving Two-Step Inequalities
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Warm Up
Solve. Check each answer.
1. 7k < 42
2. 98 > -14n
3. 9 < 12t
4. 21g < 3
k < 6
–7 < n 3 4
< t 1 7
g <

3. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Problem of the Day
It’s 15 miles from Dixon to Elmont and 20 miles from Elmont to Fairlawn. Write an inequality for x, the distance in miles from Dixon to Fairlawn.
5 ≤ x ≤ 35 (Dixon could be between Elmont and Fairlawn or Elmont could be between Dixon and Fairlawn.)

4. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Learn to solve simple two-step inequalities.

5. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
When you solve two-step equations, you can use the order of operations in reverse to isolate the variable. You can use the same process when solving two-step inequalities.

6. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Draw a closed circle when the inequality includes the point and an open circle when it does not include the point.
Remember!

7. Additional Example 1A: Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Additional Example 1A: Solving Two-Step Inequalities
Solve. Then graph the solution set on a number line. y 2
– 6 > 1 y 2
– 6 > 1
Add 6 to both sides. y 2
> 7 y 2
> (2)7
(2)
Multiply both sides by 2.
y > 14 7 14 21 –

8. Additional Example 1B: Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Additional Example 1B: Solving Two-Step Inequalities
Solve. Then graph the solution set on a number line. m –3
+ 8 m –3
5 ≥
– –8
Subtract 8 from both sides. m –3
-3 ≥ m –3
(–3) ≤
(–3)
Multiply both sides by –3, and
reverse the inequality symbol.
m ≥ 9 • –

9. Additional Example 1C: Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Additional Example 1C: Solving Two-Step Inequalities
Solve. Then graph the solution on a number line.
4y – 5 < 11
4y – 5 < 11
Add 5 to both sides.
4y < 16
4y < 16
Divide both sides by 4. 4 4
y < 4 –6 –4 –2 2 4 6

10. Additional Example 1D: Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Additional Example 1D: Solving Two-Step Inequalities
Solve. Then graph the solution set on a number line.
–4 ≥ –3x + 5
–4 ≥ –3x + 5
– –5
Subtract 5 from both sides.
–9 ≤ –3x
Divide both sides by –3, and reverse the inequality symbol.
–3 –3
x ≥ 3 3 6 9 –3 –6 –9

11. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Check It Out: Example 1A
Solve. Then graph the solution set on a number line. h 7
+ 1 > –1 h 7
+ 1 > –1
– – 1
Subtract 1 from both sides. h 7
> –2 h 7
> (7)(–2)
(7)
Multiply both sides by 7.
h > –14 7 14 21 –

12. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Check It Out: Example 1B
Solve. Then graph the solution set on a number line. m –2
+ 1 ≥ 7 m –2
+ 1 ≥ 7
– 1 –1
Subtract 1 from both sides. m –2
≥ 6 m –2
≤ (6)
(–2)
Multiply both sides by –2, and
reverse the inequality symbol.
m ≤ –12 •
–18 –12 –

13. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Check It Out: Example 1C
Solve. Then graph the solution on a number line.
C. 2y – 4 > –12
2y – 4 > –12
Add 4 to both sides.
2y > –8
2y > –8
Divide both sides by 2. 2 2
y > –4 –6 –4 –2 2 4 6

14. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Check It Out: Example 1D
Solve. Then graph the solution set on a number line.
D. –9x + 4 ≤ 31
–9x + 4 ≤ 31
– 4 –4
Subtract 4 from both sides.
–9x ≤ 27
Divide both sides by –9, and reverse the inequality symbol.
–9x ≥ 27
– –9
x ≥ –3 3 6 9 –3 –6 –9

15. Additional Example 2: Application
Course 2
12-7
Solving Two-Step Inequalities
Additional Example 2: Application
Sun-Li has $30 to spend at the carnival. Admission is $5, and each ride costs $2. What is the greatest number of rides she can ride?
Let r represent the number of rides Sun-Li can ride.
5 + 2r ≤ 30
– –5
Subtract 5 from both sides.
2r ≤ 25
Divide both sides by 2.
2r ≤ 25
r ≤ 12
252
, or 12
Sun-Li can ride only a whole number of rides, so the most she can ride is 12.

16. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Check It Out: Example 2
Brice has $30 to take his brother and his friends to the movies. If each ticket costs $4.00, and he must buy tickets for himself and his brother, what is the greatest number of friends he can invite?
Let t represent the number of tickets.
8 + 4t ≤ 30
– –8
Subtract 8 from both sides.
4t ≤ 22
Divide both sides by 4.
4t ≤ 22
t ≤ 5.5
Brice can only buy a whole number of tickets, so the most people he can invite is 5.

17. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Lesson Quiz: Part I
Solve. Then graph each solution set on a number line. –4 –2 2 –6 –8
–10
s > –7
1. 7s + 14 > –35
–62
–60
–58
–56
–64
–66
–68
y < –64 y –8
> 20 2 3 4 5 1 –1
n ≤ 3
3. 18n – 22 ≤ 32

18. Solving Two-Step Inequalities
Course 2
12-7
Solving Two-Step Inequalities
Lesson Quiz: Part II
4. A cyclist has $7.00. At the first stop on the tour, energy bars are $1.15 each, and a sports drink is $1.75. What is the greatest number of energy bars the cyclist can buy if he buys one sports drink? 4