Page 470 - Algebra 1

L E S S O N Solving Inequalities by Multiplying or
70
Dividing
Warm Up
1. Vocabulary The of an inequality in one variable is a value or
(50)
Solve.
2. 12x = -84
(21)
Graph each inequality. 4. x > -1
(50)
set of values that satisfies the inequality.
3. -7x = -91 (21)
5. x ≤ 4 (50)
New Concepts When multiplying an inequality by a positive value, the order of the inequality does not change.
Math Language
The order of the inequality refers to the direction of the inequality symbol. If
x > 2 is rewritten x < 2, then the order of the inequality has changed.
5 > 3, so 5(2) > 3(2) 8 < 12, so 8(4) < 12(4)
Multiplying by a Positive Number
Solve, graph, and check the solution for the inequality _1 x ≤ 8. 2
SOLUTION
Solve the inequality.
_1 x ≤ 8 2
(2)_1 x ≤ 8(2) Multiplication Property of Inequality for c > 0 2
Multiplication Property of Inequality for c > 0
For every real number a and b, and c > 0:
If a>b,thenac>bc. If a<b,thenac<bc.
This property is also true for ≥ and ≤.
Example
1
Hint
When checking the direction of an inequality, any value in the solution set can be substituted. Generally, it is best to select a value that can be easily computed.
x ≤ 16 Simplify.
Graph the solution on a number line.
Check
4 8 12 16 20
Online Connection www.SaxonMathResources.com
Check the endpoint. Check the direction of the inequality.
_1 x 8 _1 x 8 22
_1(16) 8 _1(14) 8 22
8=8 ✓ 7≤8 ✓ Both statements are true, so the solution is correct.
Lesson 70 455