What is the value of x?

1/2 (8x−6) = x−12

x = ?

1 answer

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

\[ \boxed{-3}. \]