If -3|x - 2| + 4 > -11, which of the following inequalities represents all possible real v… — GRE General Test

If $-3|x - 2| + 4 > -11$ , which of the following inequalities represents all possible real values of $x$ ?

-3 < x < 7

Subtracting

4

from both sides gives

-3|x - 2| > -15

. Dividing by

-3

and reversing the inequality sign results in

|x - 2| < 5

. Converting to the compound inequality

-5 < x - 2 < 5

and adding

2

to each part yields the correct interval

-3 < x < 7

Subtract 4 from both sides of the inequality

-3|x - 2| > -15

Isolate the absolute value term on the left side.

Divide both sides by

-3

and reverse the inequality sign

|x - 2| < 5

Dividing an inequality by a negative number reverses the direction of the inequality symbol.

Express the absolute value inequality as a compound inequality

-5 < x - 2 < 5

An inequality of the form

|u| < c

(where

c > 0

) is equivalent to

-c < u < c

Add 2 to all three parts of the compound inequality

-3 < x < 7

Isolate

x

to find the complete range of solution values.

Linear Inequalities and Absolute Value

Question