Preview of Grade 7 AF4.1

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Preview of Grade 7 AF4.1 Solve two-step
linear equations and inequalities in one variable
over the rational numbers, interpret the solution
or solutions in the context from which they
arose, and verify the reasonableness of the
results.
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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 1A Continued
Check
y
- 6 gt 1
2
20
20 is greater than 14 Substitute 20 for y.
2
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Additional Example 1B Solving Two-Step
Inequalities
Solve. Then graph the solution set on a number
line.
m 3
5 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
0
2
4
6
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
3 x
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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 1A Continued
Check
h
1 gt -1
7
7
7 is greater than -14 Substitute 7 for h.
7
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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.
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.
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
4t 22
Divide both sides by 4.
4 4
t 5.5
Brice can only buy a whole number of tickets, so
the most people he can invite is 5.