Question

question
solve for all values of $x$ in simplest form.
$37 = |4x - 9|$
answer attempt 1 out of 2
additional solution no solution
$x = $

Explanation:

Step1: Split absolute value equation

For $|4x-9|=37$, we have two cases:
$4x - 9 = 37$ or $4x - 9 = -37$

Step2: Solve first case

Isolate $4x$, then divide by 4.
$4x = 37 + 9 = 46$
$x = \frac{46}{4} = \frac{23}{2}$

Step3: Solve second case

Isolate $4x$, then divide by 4.
$4x = -37 + 9 = -28$
$x = \frac{-28}{4} = -7$

Answer:

$x = \frac{23}{2}$ or $x = -7$