Question

solve for v.
3|2v - 8| + 6 = 42
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
v =

Explanation:

Step1: Isolate the absolute value term

Subtract 6 from both sides:
$3|2v - 8| + 6 - 6 = 42 - 6$
$3|2v - 8| = 36$

Step2: Simplify the absolute value equation

Divide both sides by 3:
$\frac{3|2v - 8|}{3} = \frac{36}{3}$
$|2v - 8| = 12$

Step3: Split into two linear equations

Absolute value equals 12 gives two cases:
$2v - 8 = 12$ or $2v - 8 = -12$

Step4: Solve first linear equation

Add 8, then divide by 2:
$2v = 12 + 8$
$2v = 20$
$v = \frac{20}{2} = 10$

Step5: Solve second linear equation

Add 8, then divide by 2:
$2v = -12 + 8$
$2v = -4$
$v = \frac{-4}{2} = -2$

Answer:

$v = 10, -2$