Question

solve for all values of $x$ in simplest form.
$1 + 3|2x + 1| = 16$

Explanation:

Step1: Isolate the absolute - value term

Subtract 1 from both sides of the equation $1 + 3|2x + 1|=16$.
$3|2x + 1|=16 - 1$
$3|2x + 1|=15$

Step2: Solve for the absolute - value expression

Divide both sides of the equation $3|2x + 1| = 15$ by 3.
$|2x+1|=\frac{15}{3}$
$|2x + 1| = 5$

Step3: Consider two cases

Case 1: $2x+1 = 5$
Subtract 1 from both sides: $2x=5 - 1$
$2x=4$
Divide both sides by 2: $x = 2$
Case 2: $2x+1=-5$
Subtract 1 from both sides: $2x=-5 - 1$
$2x=-6$
Divide both sides by 2: $x=-3$

Answer:

$x = 2$ or $x=-3$