Question

question
solve for all values of ( x ) in simplest form.
( -5|1 - 3x| + 4 = -31 )

Explanation:

Step1: Isolate the absolute value term

Subtract 4 from both sides:
$-5|1-3x| = -31 - 4$
$-5|1-3x| = -35$
Divide both sides by -5:
$|1-3x| = 7$

Step2: Split into two linear equations

Absolute value equals 7 means two cases:
Case 1: $1-3x = 7$
Case 2: $1-3x = -7$

Step3: Solve Case 1

Subtract 1 from both sides:
$-3x = 7 - 1$
$-3x = 6$
Divide by -3:
$x = \frac{6}{-3} = -2$

Step4: Solve Case 2

Subtract 1 from both sides:
$-3x = -7 - 1$
$-3x = -8$
Divide by -3:
$x = \frac{-8}{-3} = \frac{8}{3}$

Answer:

$x=-2$ and $x=\frac{8}{3}$