Student Help
STUDY TIP
A number is a solution
of a compound
inequality with or if the
number is a solution of
either inequality.
EXAMPLE
2
Solve a Compound Inequality with Or
Solve the compound inequality x 4 ≤ 3 or 2x > 18. Then graph the solution.
Solution
A solution of this compound inequality is a solution of either of its parts. You
can solve each part separately using the methods of Lessons 6.1 and 6.2.
x4≤3
or 2x > 18
2x
2
Write original inequality.
18
2
x 4 4 ≤ 3 4 or > x≤7
ANSWER 䊳
or
x>9
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Simplify.
The solution is all real numbers less than or equal to 7 or greater
than 9. The graph of the solution is shown below.
5
Student Help
Isolate x.
EXAMPLE
3
6
7
8
9
10
11
Solve a Multi-Step Compound Inequality
Solve the compound inequality 3x 1 < 4 or 2x 5 > 7. Then graph
the solution.
Solution
Solve each of the parts using the methods of Lesson 6.3.
3x 1 < 4
2x 5 > 7
or
Write original inequality.
3x 1 1 < 4 1 or 2x 5 5 > 7 5
ANSWER 䊳
Isolate x.
3x < 3
or
2x > 12
Simplify.
3x 3
< 3
3
or
2x 12
> 2
2
Solve for x.
x<1
or
x>6
Simplify.
The solution is all real numbers less than 1 or greater than 6.
The graph of the solution is shown below.
1
0
1
2
3
4
5
6
7
Solve a Compound Inequality with Or
Tell whether 5 is a solution of the inequality.
7. x < 5 or x > 4
8. x ≤ 3 or x > 0
Solve the inequality. Then graph the solution.
9. x 4 < 8 or x 3 > 5
6.5
10. 2x 3 ≤ 1 or 3x 5 > 1
Solving Compound Inequalities Involving “Or”
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