Page 553 - Algebra 1

L E S S O N Solving Multi-Step Compound Inequalities 82
Warm Up
1. Vocabulary A(n)
(73) with the word and or or.
Solve each inequality. 2. 8x > 6x - 12
(81)
3. -1 -(-7) ≤ 3(y - 6) (77)
4. x - 2 < -7 OR 2x ≥ 11 (73)
is made up of two inequalities combined
5. Multiple Choice Which compound inequality is equivalent to 6 ≤ -2x < 22? (73) A -11 < x ≤ -3 B -11 > x ≥ -3
C 8 ≤ x < 24 D -24 < x ≤ -8
New Concepts Inequalities can be solved in two or more steps using inverse operations. A compound inequality is made of two inequalities joined by the word AND
or OR.
-2 < x AND x ≤ 5 x ≤ -4 OR x ≥ 1 Solving Multi-Step Compound Inequalities
Example
1
Hint
The term AND indicates that the solution must satisfy both inequalities. The term OR indicates that the solution must satisfy either inequality.
Solve and graph each inequality.
a. 4x - 7 < 3 OR 2x - 19 > -7
SOLUTION Isolate the variable in both inequalities. 4x - 7 < 3 OR 2x - 19 > - 7
+__7 +__7 +_1_9 4x < 10 OR 2x > 12
4x < 10 OR 2x > 12 ____
4422
x < 2_1 OR x > 6 2
+_1_9
Addition Property of Inequality Simplify.
Division Property of Inequality
0 1 2 3 4 5 6 7
b. -9≤3x-4+2x≤11
SOLUTION Isolate the variable between the inequality signs. -9 ≤ 3x - 4 + 2x ≤ 11
Caution
Be sure to perform inverse operations on all three parts of the compound inequality.
+__4 +__4 +__4 -5 ≤ 3x + 2x ≤ 15
-5 ≤ 5x ≤ 15 ___
555 -1 ≤ x ≤ 3
Addition Property of Inequality Simplify.
Division Property of Inequality
-2 0 2 4
538 Saxon Algebra 1