Question

What is the value of x?
1/2 (8x−6) = x−12

x = ?

Answer 1

To solve the equation

\[
\frac{1}{2} (8x - 6) = x - 12,
\]

first, remove the fraction by multiplying both sides of the equation by 2:

\[
8x - 6 = 2(x - 12).
\]

Next, distribute the 2 on the right side:

\[
8x - 6 = 2x - 24.
\]

Now, isolate the variable \(x\) by first moving all terms involving \(x\) to one side and constant terms to the other side. Subtract \(2x\) from both sides:

\[
8x - 2x - 6 = -24.
\]

This simplifies to:

\[
6x - 6 = -24.
\]

Next, add 6 to both sides to isolate the term with \(x\):

\[
6x = -24 + 6,
\]

which simplifies to:

\[
6x = -18.
\]

Finally, divide both sides by 6:

\[
x = -3.
\]

Thus, the value of \(x\) is

\[
\boxed{-3}.
\]