Question

what are the solutions of the following equation?
$15|x - 7| + 4 = 10|x - 7| + 4$
choose 1 answer:
a $x = -\frac{5}{7}$ or $x = \frac{5}{7}$
b $x = \frac{7}{5}$ or $x = -\frac{7}{5}$
c $x = 5$ or $x = -5$
d only $x = 7$
e there are no solutions

Explanation:

Step1: Subtract 4 from both sides

$15|x - 7| + 4 - 4 = 10|x - 7| + 4 - 4$
Simplifies to: $15|x - 7| = 10|x - 7|$

Step2: Subtract \(10|x - 7|\) from both sides

$15|x - 7| - 10|x - 7| = 10|x - 7| - 10|x - 7|$
Simplifies to: $5|x - 7| = 0$

Step3: Divide both sides by 5

$\frac{5|x - 7|}{5} = \frac{0}{5}$
Simplifies to: $|x - 7| = 0$

Step4: Solve the absolute value equation

If \(|a| = 0\), then \(a = 0\). So \(x - 7 = 0\), which gives \(x = 7\).

Answer:

D. Only \(x = 7\)