Question

solve $|6x + 3| = 21$
a. $x = -3$ and $x = 4$
b. $x = 3$ and $x = -4$
c. $x = 3$ and $x = -3$
d. $x = -3$ and $x = -4$

Explanation:

Step1: Split absolute value equation

For $|6x+3|=21$, we get two cases:
$6x+3=21$ or $6x+3=-21$

Step2: Solve first case for x

Subtract 3, then divide by 6:
$6x=21-3=18$
$x=\frac{18}{6}=3$

Step3: Solve second case for x

Subtract 3, then divide by 6:
$6x=-21-3=-24$
$x=\frac{-24}{6}=-4$

Answer:

B. $x = 3$ and $x = -4$