5-4 Solving Inequalities
Solve each inequality. Check your solution.
y + 7 12
The solution is y
Check:
y
5.
5
b + 20 > 13
The solution is b > 33.
Check:
b > 33
7 < x + ( 3)
The solution is x > 4.
Check:
x> 4
Solve
each- Powered
inequality.
Graph
eSolutions
Manual
by Cognero
d
9.3
12.5
the solution on a number line.
Page 1
5-4 Solving Inequalities
x> 4
Solve each inequality. Graph the solution on a number line.
d 9.3 12.5
The solution is d
d
21.8.
21.8
>f
The solution is f < 4.
Since the inequality symbol is <, draw an open dot at 4 with an arrow to the left.
f<4
g
22
40
The solution is g
18.
eSolutions Manual - Powered by Cognero
18 with an arrow to the left.
Page 2
f<4
5-4 Solving Inequalities
g
22
40
The solution is g
g
18.
18 with an arrow to the left.
18
JOBS Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how many hours she
needs to work to earn at least $120.
Number of hours worked times hourly payment rate must be greater than or equal to $120.
Let h = the number of hours Isabel must work.
So, Isabel must work at least 16 hours to earn $120.
7.5t
120; at least 16 hours
Solve each inequality. Graph the solution on a number line.
20 < 4t
The solution is t < 5.
Since the inequality symbol is <, draw an open dot at 5 with an arrow to the left.
t<5
eSolutions Manual - Powered by Cognero
Page 3
So, Isabel must work at least 16 hours to earn $120.
5-4 Solving Inequalities
7.5t
120; at least 16 hours
Solve each inequality. Graph the solution on a number line.
20 < 4t
The solution is t < 5.
Since the inequality symbol is <, draw an open dot at 5 with an arrow to the left.
t<5
8z
24
The solution is z
z
3.
3
18 >
g
eSolutions
- Powered
Cognero
TheManual
solution
is g > by27.
Since the inequality symbol is >, draw an open dot at 27 with an arrow to the right.
Page 4
z
3
5-4 Solving Inequalities
18 >
g
The solution is g > 27.
Since the inequality symbol is >, draw an open dot at 27 with an arrow to the right.
g > 27
Solve each inequality. Check your solution.
a + 18 < 40
The solution is a < 22.
Check:
a < 22
h
12 > 52
The solution is h > 64.
Check:
eSolutions Manual - Powered by Cognero
Page 5
5-4 aSolving
Inequalities
< 22
h
12 > 52
The solution is h > 64.
Check:
h > 64
y
4.2
6.5
The solution is y
Check:
y
10.7.
10.7
g + 5.9
10
The solution is g
Check:
g
4.1
p
14 > 12
4.1.
eSolutions Manual - Powered by Cognero
Page 6
5-4 Solving Inequalities
g
4.1
p
14 > 12
The solution is p > 26.
Check:
p > 26
x + 3.75 < 5
The solution is x < 1.25.
Check:
x < 1.25
n
0.1
1.4
The solution is n
Check:
n
1.5.
1.5
7 >z +
eSolutions Manual - Powered by Cognero
Page 7
5-4 Solving Inequalities
n
1.5
7 >z +
The solution is z <
.
Check:
z<
22
c
2.1
The solution is c
Check:
c
13
24.1.
24.1
9+b
The solution is b
Check:
4.
eSolutions Manual - Powered by Cognero
Page 8
5-4 Solving Inequalities
c
13
24.1
9+b
The solution is b
Check:
b
4.
4
<b
The solution is b >
.
Check:
b>
t+
<
eSolutions Manual - Powered by Cognero
The solution is t <
.
Page 9
5-4 bSolving
Inequalities
>
t+
<
The solution is t <
.
Check:
t<
ARCADES Montel spends $0.75 every time he plays his favorite video game. If he has $10, write and solve an
inequality to find how many video games he can play.
Number of times Montel plays the video game times $0.75 must be less than or equal to $10.
Let v = the number of times Montel plays the video game.
So, Montel can play his favorite video game at most 13 times.
at most 13 games
ANIMALS Write and solve an inequality to find the swimming rate of a manatee that swims at least 15 miles in 3
hours.
The distance the manatee swims is less than or equal to the rate it swims times 3 hours.
Let r = the manatee s rate.
eSolutions Manual - Powered by Cognero
The manatee swims at a rate of at least 5 miles per hour.
Page 10
So, Montel can play his favorite video game at most 13 times.
5-4 Solving Inequalities
at most 13 games
ANIMALS Write and solve an inequality to find the swimming rate of a manatee that swims at least 15 miles in 3
hours.
The distance the manatee swims is less than or equal to the rate it swims times 3 hours.
Let r = the manatee s rate.
The manatee swims at a rate of at least 5 miles per hour.
3m
15; at least 5 miles per hour
Solve each inequality. Graph the solution on a number line.
4x > 36
The solution is x > 9.
Since the inequality symbol is >, draw an open dot at 9 with an arrow to the right.
x> 9
7y
49
The solution is y
7.
7 with an arrow to the left.
7
y
eSolutions Manual - Powered by Cognero
5m
Page 11
x> 9
5-4 Solving Inequalities
7y
49
The solution is y
7.
7 with an arrow to the left.
7
y
5m
The solution is m
m
3.
3 with an arrow to the left.
3
2p < 3
The solution is p > 1.5.
Since the inequality symbol is >, draw an open dot at 1.5 with an arrow to the right.
p > 1.5
eSolutions Manual - Powered by Cognero
45
10r
Page 12
3
m
5-4 Solving Inequalities
2p < 3
The solution is p > 1.5.
Since the inequality symbol is >, draw an open dot at 1.5 with an arrow to the right.
p > 1.5
45
10r
The solution is r
4.5.
4.5 with an arrow to the left.
4.5
r
11t
The solution is t
t
6.
6
eSolutions Manual - Powered by Cognero
y > 63
Page 13
4.5
r
5-4 Solving Inequalities
11t
The solution is t
t
6.
6
y > 63
The solution is y > 18.
Since the inequality symbol is >, draw an open dot at 18 with an arrow to the right.
y > 18
m
The solution is
eSolutions Manual - Powered by Cognero
.
Page 14
y > 18
5-4 Solving Inequalities
m
.
The solution is
b
The solution is b
b
2.
2
>3
eSolutions Manual - Powered by Cognero
Page 15
2
b
5-4 Solving Inequalities
>3
The solution is x < 12.
Since the inequality symbol is <, draw an open dot at 12 with an arrow to the left.
x < 12
c
The solution is
.
a
eSolutions Manual - Powered by Cognero
Page 16
5-4 Solving Inequalities
a
The solution is
.
eSolutions Manual - Powered by Cognero
Page 17