Page 618 - Algebra 1

Example
2
Isolating the Absolute Value to Solve
Solve and graph each inequality.
a. x +7.4≤9.8
SOLUTION
Begin by isolating the absolute value. x + 7.4 ≤ 9.8
-__7._4 -__7._4 Subtraction Property of Inequality x ≤ 2.4 Simplify.
Since the absolute value of x is less than or equal to 2.4, it is 2.4 units or less from zero.
-3 -2 -1 0 1 2 3
The solution can be written x ≥ -2.4 AND x ≤ 2.4 or -2.4 ≤ x ≤ 2.4.
x _
b. 4>2
SOLUTION
Begin by isolating the absolute value.
Multiplication Property of Inequality Simplify.
x _
4>2 _
-12 -8 -4 0 4 8 12 The solution is x > 8 OR x < -8.
c. -2 x < -6
SOLUTION
Begin by isolating the absolute value.
4 · x > 2 · 4 4
x > 8
The absolute value of x is greater than 8, so it is more than 8 units from zero.
Caution
Be sure to reverse
the direction of the inequality sign if you multiply or divide by a negative number when solving the inequality.
Online Connection www.SaxonMathResources.com
-2 > -2 Division Property of Inequality x > 3 Simplify.
Since the absolute value of x is greater than 3, it is more than 3 units from zero.
-4 -2 0 2 4 The solution is x > 3 OR x < -3.
-2 x < -6
-2 x
_ _-6
Lesson 91 603