A solution of an inequality in one variable is a value of the variable that makes
the inequality true. To solve such an inequality, you may have to rewrite it as a
simpler equivalent inequality. Equivalent inequalities have the same solutions.
Adding the same number to, or subtracting the same number from, each side of
an inequality in one variable produces an equivalent inequality.
3<7
32<72
0
1
2
3
2
5
3
4
5
6
7
2
9
7
8
9
10
5<9
PROPERTIES OF INEQUALITY
Student Help
STUDY TIP
The properties are
stated for > and <
inequalities. They are
also true for ≥ and ≤
inequalities.
Addition Property of Inequality
If a > b, then a c > b c.
If a < b, then a c < b c.
For all real numbers a, b, and c:
Subtraction Property of Inequality
If a > b, then a c > b c.
If a < b, then a c < b c.
For all real numbers a, b, and c:
EXAMPLE
2
Use Subtraction to Solve an Inequality
Solve x 5 ≥ 3. Then graph the solution.
Student Help
Solution
STUDY TIP
To check solutions,
choose numbers that
make the arithmetic
easy. For Example 2
you could check zero
as a value of x.
?
05≥3
5≥3✔
x5≥3
Write original inequality.
x55≥35
x ≥ 2
ANSWER 䊳
Subtract 5 from each side.
(Subtraction Property of Inequality)
Simplify.
The solution is all real numbers greater than or equal to 2. Check
several numbers that are greater than or equal to 2 in the original
inequality. The graph of the solution is shown below.
3
2
1
0
1
2
3
You cannot check all the solutions of an inequality. Instead, choose several
solutions. Substitute them in the original inequality. Be sure they make it true.
Then choose several numbers that are not solutions. Be sure they do not make the
original inequality true.
Use Subtraction to Solve an Inequality
Solve the inequality. Then graph the solution.
5. x 4 < 7
324
Chapter 6
Solving and Graphing Linear Inequalities
6. n 6 ≥ 2
7. 5 > a 5