Download Holt CA Course 1 - Jefferson School District

11-8 Solving Two-Step Inequalities
California
Standards
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.
Holt CA Course 1
11-8 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.
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Remember!
Draw a closed circle when the inequality includes
the point and an open circle when it does not
include the point.
Holt CA Course 1
11-8 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
+6 +6
y
>7
2
y > (2)7
(2) 2
Add 6 to both sides.
Multiply both sides by 2.
y > 14
– 21
Holt CA Course 1
– 14
–7
0
7
14
21
11-8 Solving Two-Step Inequalities
Additional Example 1A Continued
Check
y -6>1
2
?
20
-6>1
2
4>1
Holt CA Course 1
20 is greater than 14
Substitute 20 for y.
11-8 Solving Two-Step Inequalities
Additional Example 1B: Solving Two-Step
Inequalities
Solve. Then graph the solution set on a number line.
5≥ m +8
–3
m
5≥
+8
–3
–8
–8
m
-3 ≥
–3
m
(–3)
(–3)(–3) ≤
–3
m≥9
Holt CA Course 1
Subtract 8 from both sides.
Multiply both sides by –3, and
reverse the inequality symbol.
–3
0
3
6
•
9
12
15
11-8 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
+5 +5
4y
< 16
4y
4
–6
Holt CA Course 1
Add 5 to both sides.
< 16
4
y<4
–4 –2
0
Divide both sides by 4.
º
2 4
6
11-8 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
–9 ≤ –3x
–3
–3
3≤x
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–5
Subtract 5 from both sides.
Divide both sides by –3,
and reverse the inequality
symbol.
–9 –6 –3
0
3 6
9
11-8 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
–1
h
> –2
7
h > (7)(–2)
(7) 7
Subtract 1 from both sides.
Multiply both sides by 7.
h > –14
– 21
Holt CA Course 1
– 14
–7
0
7
14
21
11-8 Solving Two-Step Inequalities
Check It Out! Example 1A Continued
Check
h
+ 1 > -1
7
?
7
+ 1 > -1 7 is greater than -14
7
Substitute 7 for h.
2>1
Holt CA Course 1
11-8 Solving Two-Step Inequalities
Check It Out! Example 1B
Solve. Then graph the solution set on a number line.
m +1≥7
–2
m +1≥7
–2
– 1 –1
Subtract 1 from both sides.
m
≥ 6
–2
(–2) m ≤ (–2)(6) Multiply both sides by –2, and
–2
reverse the inequality symbol.
m ≤ –12
Holt CA Course 1
•
–18 –12 –6
0
6
12
18
11-8 Solving Two-Step Inequalities
Check It Out! Example 1C
Solve. Then graph the solution on a number line.
2y – 4 > –12
2y – 4 > –12
+4 +4
2y
> –8
2y
2
º
> –8
2
y > –4
–6 –4 –2
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0
2 4
Add 4 to both sides.
Divide both sides by 2.
6
11-8 Solving Two-Step Inequalities
Check It Out! Example 1D
Solve. Then graph the solution set on a number line.
–9x + 4 ≤ 31
–9x + 4 ≤ 31
– 4 –4
–9x
≤ 27
–9x ≥ 27
–9
–9
x ≥ –3
–9 –6 –3
Holt CA Course 1
0
3 6
Subtract 4 from both sides.
Divide both sides by –9,
and reverse the inequality
symbol.
9
11-8 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
–5
Subtract 5 from both sides.
2r ≤ 25
Divide both sides by 2.
2r ≤ 25
2
2
1
25
,
or
12
r≤
2
2
Sun-Li can ride only a whole number of rides, so the most
she can ride is 12.
Holt CA Course 1
11-8 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
–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.
Holt CA Course 1