Question

question
solve for all values of x in simplest form.
1 + 5|4 + x| = 46

Explanation:

Step1: Isolate absolute value term

Subtract 1 from both sides:
$1 + 5|4+x| - 1 = 46 - 1$
$5|4+x| = 45$

Step2: Simplify absolute value equation

Divide both sides by 5:
$\frac{5|4+x|}{5} = \frac{45}{5}$
$|4+x| = 9$

Step3: Split into two linear equations

For absolute value equality $|A|=B$, solve $A=B$ and $A=-B$:
$4+x = 9$ and $4+x = -9$

Step4: Solve first linear equation

Subtract 4 from both sides:
$x = 9 - 4$
$x = 5$

Step5: Solve second linear equation

Subtract 4 from both sides:
$x = -9 - 4$
$x = -13$

Answer:

$x = 5$ and $x = -13$