Question

what are the solutions of the following equation?
$8 = 3|x - 7| + 4$
choose 1 answer:
a $x = -dfrac{25}{3}$ or $x = dfrac{25}{3}$
b $x = dfrac{17}{3}$ or $x = dfrac{25}{3}$
c only $x = dfrac{25}{3}$
d there are no solutions.

Explanation:

Step1: Isolate the absolute value term

Subtract 4 from both sides:
$8 - 4 = 3|x - 7| + 4 - 4$
$4 = 3|x - 7|$

Step2: Solve for $|x-7|$

Divide both sides by 3:
$\frac{4}{3} = |x - 7|$

Step3: Split into two cases

Case 1: $x - 7 = \frac{4}{3}$
Case 2: $x - 7 = -\frac{4}{3}$

Step4: Solve Case 1

Add 7 to both sides:
$x = 7 + \frac{4}{3} = \frac{21}{3} + \frac{4}{3} = \frac{25}{3}$

Step5: Solve Case 2

Add 7 to both sides:
$x = 7 - \frac{4}{3} = \frac{21}{3} - \frac{4}{3} = \frac{17}{3}$

Answer:

B. $x = \frac{17}{3}$ or $x = \frac{25}{3}$