Page 694 - Algebra 1

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b. ⎢x -4>-2
5
SOLUTION
_
⎢x -4>-2
5
⎢x > 2 _
5
⎢x > 10
Add 4 to each side. Multiply each side by 5.
x < -10 OR x > 10 Write as a compound inequality.
-30 -20 -10 0 10 20 30
Hint
Reverse the direction of the inequality symbol when dividing each side of an inequality by a negative number.
c. -10⎢x + 54 ≥ -21
SOLUTION
-10⎢x + 54 ≥ -21 -10⎢x ≥ -75
⎢x ≤ 7.5 -7.5 ≤ x ≤ 7.5
Subtract 54 from each side. Divide each side by -10.
Write as a compound inequality.
-10 -8 -6 -4 -2 0 2 4 6 8 10
Algebraic expressions within the absolute-value symbols may have one or more operations on the variable. So, after the absolute-value expression is isolated, solving the resulting compound inequality requires additional steps.
Solving Inequalities with One Operation Inside Absolute-Value Symbols
Solve and graph the inequality.
⎢x + 5 - 1 > 7
SOLUTION
Isolate the absolute-value expression ⎢x + 5 . Then write it as a compound inequality.
⎢x + 5 - 1 > 7
⎢x + 5 > 8 Add 1 to each side.
x+5<-8 OR x+5>8 Writeasacompoundinequality.
Solve each part of the compound inequality for x.
x<-13 OR x>3 Subtract5fromeachsideofthetwo inequalities.
-20 -10 0 10 20
Example
2
Lesson 101 679