Question $-4|w-16|+9=-39$ A) $w=\{-4,-28\}$ cowboy boo B) $w=\{4,28\}$ hot rollers C) $w=\{-4,28\}$ snow pants D) $w=\{-28,28\}$ hair nets E) $w=\{-28,4\}$ clown shoes

Studdy Solution

STEP 1

1. The equation involves an absolute value expression.
2. We will isolate the absolute value term and solve for the variable $w$ .

STEP 2

1. Isolate the absolute value expression.
2. Solve the resulting equation for the absolute value.
3. Solve for $w$ by considering both cases of the absolute value.

STEP 3

First, isolate the absolute value term by subtracting 9 from both sides of the equation:
$-4|w-16| + 9 = -39$ $-4|w-16| = -39 - 9$ $-4|w-16| = -48$

STEP 4

Next, divide both sides by $-4$ to solve for the absolute value expression:
$|w-16| = \frac{-48}{-4}$ $|w-16| = 12$

STEP 5

Now, solve for $w$ by considering both cases of the absolute value equation:
Case 1: $w - 16 = 12$
$w - 16 = 12$ $w = 12 + 16$ $w = 28$
Case 2: $w - 16 = -12$
$w - 16 = -12$ $w = -12 + 16$ $w = 4$
The solutions for $w$ are:
$w = \{4, 28\}$
The correct answer is:
B) $w = \{4, 28\}$ hot rollers

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