Question

Solve for x.

x - 4 = 1/4 (8x - 16)

Answer 1

To solve the equation \( x - 4 = \frac{1}{4} (8x - 16) \), we start by simplifying the right side of the equation.

First, distribute \(\frac{1}{4}\) into the expression \(8x - 16\):

\[
\frac{1}{4} (8x - 16) = \frac{1}{4} \cdot 8x - \frac{1}{4} \cdot 16 = 2x - 4
\]

Now we can rewrite the equation:

\[
x - 4 = 2x - 4
\]

Next, we can eliminate \(-4\) from both sides of the equation:

\[
x - 4 + 4 = 2x - 4 + 4
\]
\[
x = 2x
\]

To isolate \(x\), subtract \(x\) from both sides:

\[
x - 2x = 0
\]
\[
-x = 0
\]

Multiply both sides by \(-1\):

\[
x = 0
\]

Therefore, the solution to the equation is:

\[
\boxed{0}
\]