Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Solve. Check each answer. 1. 7k lt 42 2.
98 gt -14n 3. 9 lt 12t 4. 21g lt 3
k lt 6
7 lt n
3 4
lt t
1 7
g lt
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Problem of the Day Its 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.)
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Learn to solve simple two-step inequalities.
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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.
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Additional Example 1A Solving Two-Step
Inequalities
Solve. Then graph the solution set on a number
line.
y 2
6 gt 1
6 6
Add 6 to both sides.
Multiply both sides by 2.
y gt 14
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Additional Example 1B Solving Two-Step
Inequalities
Solve. Then graph the solution set on a number
line.
m 3
8


8 8
Subtract 8 from both sides.
Multiply both sides by 3, and reverse the
inequality symbol.
m 9

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Additional Example 1C Solving Two-Step
Inequalities
Solve. Then graph the solution on a number line.
4y 5 lt 11
4y 5 lt 11
5 5
Add 5 to both sides.
4y lt 16
4y lt 16
Divide both sides by 4.
4
4
y lt 4
º
2
4
6
0
2
4
6
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Additional Example 1D Solving Two-Step
Inequalities
Solve. Then graph the solution set on a number
line.
4 3x 5
4 3x 5
5 5
Subtract 5 from both sides.
9 3x
Divide both sides by 3, and reverse the
inequality symbol.
3 3
x 3
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Check It Out Example 1A
Solve. Then graph the solution set on a number
line.
h 7
1 gt 1
1 1
Subtract 1 from both sides.
Multiply both sides by 7.
h gt 14
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Check It Out Example 1B
Solve. Then graph the solution set on a number
line.
m 2
1 7


1 1
Subtract 1 from both sides.
Multiply both sides by 2, and reverse the
inequality symbol.
m 12

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Check It Out Example 1C
Solve. Then graph the solution on a number line.
C. 2y 4 gt 12
2y 4 gt 12
4 4
Add 4 to both sides.
2y gt 8
2y gt 8
Divide both sides by 2.
2
2
y gt 4
º
2
4
6
0
2
4
6
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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 9
x 3
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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 5
Subtract 5 from both sides.
2r 25
Divide both sides by 2.
2r 25
2 2
Sun-Li can ride only a whole number of rides, so
the most she can ride is 12.
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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 8
Subtract 8 from both sides.
4t 22
Divide both sides by 4.
4t 22
4 4
t 5.5
Brice can only buy a whole number of tickets, so
the most people he can invite is 5.
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Lesson Quiz Part I
Solve. Then graph each solution set on a number
line.
1. 7s 14 gt 35
y 8
2. 12 gt 20
3. 18n 22 32
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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?
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