Which of the following is the solution set for the inequality |5 - 2x| < 9? — ACT

Which of the following is the solution set for the inequality $|5 - 2x| < 9$ ?

-2 < x < 7

The correct solution is found by setting up the compound inequality

-9 < 5 - 2x < 9

. Subtracting

5

from all parts gives

-14 < -2x < 4

. Finally, dividing by

-2

and reversing the inequality signs yields the interval

-2 < x < 7

Rewrite the absolute value inequality as a compound inequality.

-9 < 5 - 2x < 9

An absolute value inequality of the form

|u| < c

represents all points within distance

c

from

0

, which translates to

-c < u < c

Subtract

5

from all three parts of the inequality.

-14 < -2x < 4

To isolate the variable term, we perform the inverse operation of adding

5

, which is subtracting

5

Divide all three parts by

-2

and reverse the inequality signs.

-2 < x < 7

Dividing by a negative number reverses the inequality direction. Doing so gives

7 > x > -2

, which is conventionally written as

-2 < x < 7

Solving absolute value inequalities of the form

|ax + b| < c

Soru