Download 4 Solve Multi-Step Compound Inequalities 5 Reverse Both Inequalities

EXAMPLE
4
Solve Multi-Step Compound Inequalities
Solve 3 ≤ 2x 1 ≤ 5. Then graph the solution.
Solution
Isolate the variable between the inequality symbols.
3 ≤ 2x 1 ≤ 5
Write original inequality.
3 1 ≤ 2x 1 1 ≤ 5 1
4 ≤ 2x ≤ 4
Simplify.
4 2x 4
≤ ≤ 2
2
2
Divide each expression by 2.
2 ≤ x ≤ 2
ANSWER 䊳
Subtract 1 from each expression.
Simplify.
The solution is all real numbers greater than or equal to 2 and less
than or equal to 2. The graph of the solution is shown below.
4 3 2 1
EXAMPLE
5
0
1
2
3
4
Reverse Both Inequalities
Solve 2 < 2 x < 1. Then graph the solution.
Student Help
Solution
STUDY TIP
When you multiply or
divide each expression
of a compound
inequality by a
negative number,
remember to reverse
both inequalities.
Isolate the variable x between the two inequality symbols.
2 < 2 x < 1
Write original inequality.
2 2 < 2 x 2 < 1 2
Add 2 to each expression.
0 < x < 3
Simplify.
1(0) > 1(x) > 1(3)
0 > x > 3
ANSWER 䊳
Multiply each expression by 1 and
reverse both inequalities.
Simplify.
The solution is all real numbers greater than 3 and less than 0.
The graph of the solution is shown below.
5 4 3 2 1
0
1
2
A compound inequality is usually written in a way that reflects the order of
numbers on a number line. In Example 5 above, the solution would usually be
written 3 < x < 0.
Solve Compound Inequalities with And
Solve the inequality. Then graph the solution.
7. 3 ≤ 2x 3 ≤ 7
344
Chapter 6
Solving and Graphing Linear Inequalities
8. 6 ≤ 3x ≤ 12
9. 3 ≤ 4 x ≤ 2