Page 547 - Algebra 1

L E S S O N Solving Inequalities with Variables on
81
Both Sides
Warm Up
1. Vocabulary An equation or inequality that is always true is called a(n)
(28)
(identity, solution). Solve each inequality.
2. 6x ≤ 42 (70)
4. 2p + 3 < -25 (77)
_
3. - 3k > _5
(70) 4 8
5. 5x - 3 - 7x ≤ -9
(77)
New Concepts Sometimes an inequality will have a variable on both sides of the inequality sign. A solution to such an inequality is found by transforming the inequality
so that the variable is isolated on one side of the inequality.
Solving Inequalities with Variables on Both Sides
Solve and graph each inequality.
a. 2x + 7 > -5x + 21 SOLUTION
Example
1
2x + 7 > -5x + 21 7x + 7 > 21
7x > 14 x > 2
Add 5x to both sides. Subtract 7 from both sides. Divide both sides by 7.
Graph the inequality on a number line.
0246
____ b. -5b+ 5 ≥b- 9
8 16 8 16
SOLUTION
____ -5b+ 5 ≥b- 9
Hint
The order of the inequality is reversed when the inequality is multiplied or divided by a negative number.
8 16 8 16 ____
-6b + 5 ≥ - 9 Subtract b from both sides. 81616 8
___
- 6b ≥ - 14 Subtract 5 from both sides.
8 16 16
_ -8 b ≤ 7 Multiply both sides by _ .
66 Graph the inequality on a number line.
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