Question

1. noah is solving the equation below. find the value of x that makes the equation true.

\\(\frac{1}{4}x - 8 = \frac{1}{8}x + 8\\)

Explanation:

Step1: Subtract $\frac{1}{8}x$ from both sides

To eliminate the $\frac{1}{8}x$ term on the right, we subtract $\frac{1}{8}x$ from both sides.
$\frac{1}{4}x - \frac{1}{8}x - 8 = \frac{1}{8}x - \frac{1}{8}x + 8$
Simplifying the $x$ terms: $\frac{2}{8}x - \frac{1}{8}x = \frac{1}{8}x$, so we get $\frac{1}{8}x - 8 = 8$

Step2: Add 8 to both sides

To isolate the term with $x$, we add 8 to both sides.
$\frac{1}{8}x - 8 + 8 = 8 + 8$
Simplifying both sides: $\frac{1}{8}x = 16$

Step3: Multiply both sides by 8

To solve for $x$, we multiply both sides by 8.
$8\times\frac{1}{8}x = 16\times8$
Simplifying: $x = 128$

Answer:

$x = 128$