How do you solve $-5|-2x + -3| + 2 = -33$ ?

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Answer 1 · 2017-06-12T03:22:50

Given: $-5|-2x -3| + 2 = -33$

Subtract 2 from both sides:

$-5|-2x + -3| = -35$

Divide both sides by -5:

$|-2x + -3| = 7" [1]"$

Using the definition of the absolute value function,

$|A| = {(A; A>=0),(-A;A < 0):}$

We can write the following:

$|-2x -3| = {(-2x-3; -2x-3>= 0),(2x+3;-2x-3<0):}$

Simplify the inequalities:

$|-2x -3| = {(-2x-3; -2x>= 3),(2x+3;-2x<3):}$

$|-2x -3| = {(-2x-3; x<= -3/2),(2x+3;x> -3/2):}$

Substitute both into equation [1]:

$-2x -3 = 7; x <= -3/2$ and $2x + 3 = 7; x > -3/2$

$-2x = 10; x <= -3/2$ and $2x = 4; x > -3/2$

$x = -5; x <= -3/2$ and $x = 2; x > -3/2$

Check in the original equation:

$-5|-2(-5) -3| + 2 = -33$ and $-5|-2(2) -3| + 2 = -33$

$-5|7| + 2 = -33$ and $-5|-7| + 2 = -33$

$-33 = -33$ and $-33 = -33$

Both values check.

$x = -5$ and $x = 2$

How do you solve -5|-2x + -3| + 2 = -33-5|-2x + -3| + 2 = -33?