Solving One and Two-Step
Inequalities
#43
VOCABULARY
An inequality is a statement that two
quantities are not equal. The quantities
are compared by using one of the following
symbols:
<
>
≤
≥
≠
An inequality may contain a variable, as in
x > 3. A solution of an equality is any value
of the variable that makes the statement true.
Example 1: Graphing Inequalities
Graph the solutions of each inequality on a
number line.
A. t > 1
2
3
4
5
6
7
8
B. y  11
9
10
11
12
13
14
15
Example 2: Solving Inequalities with Addition or
Subtraction
Solve and graph each inequality.
x–3≥5
–1
0
1
2
3
4
5
6
7
8
9 10 11
Example 3
Solve and graph each inequality.
5<x+3
1
2
3
4
5
6
7
Example 4: Solving Inequalities with Multiplication or
Division
Solve and graph each inequality.
8z < 32
–1
0
1
2
3
4
5
6
7
8
9 10 11
The empty circle at 4 shows that 4 is not a solution.
Example 5
Graph the solution of the inequality on a
number line.
a >4
4
13 14 15 16 17 18 19
Example 6: Write an Inequality to Represent the
Situation
Six friends go to a restaurant. They have a gift
certificate for $150. They plan to share it equally
and spend no additional money. Write an
inequality to describe how much each friend can
spend.
Example 7
Derek must log at least 20 hours of flight time
for a sport pilot certificate. So far, he has logged
7 hours. Write and solve an inequality to
describe how much more flight time Derek needs
to log.
Example 8: Solving Two-Step Inequalities
Solve and graph each inequality.
3y + 6 > 12
–1
0
1
2
3
4
5
6
7
8
9 10 11
Example 9: Solving Two-Step Inequalities
Solve and graph each inequality.
t + 3  12
3
24 25 26 27 28 29 30 31 32 33 34 35 36
Example 10
Solve and graph each inequality.
2m-3<7
0
1
2
3
4
5
6
7
8
9 10
Example 11: Problem Solving Application
The cost to rent a party room is $70.
There is an additional fee of $8 per
guest. How many guests can Jesse
invite if he can spend no more than
$150?
Example 12
Hanley Ramirez plays baseball for the Florida
Marlins. His batting average is his total hits
divided by total at-bats, to the nearest
thousandth. With two games remaining in the
2008 season, he had 173 hits and 581 atbats. If he gets 8 more at-bats, how many
more hits must he get to have an average of
at least .300?