Question

Solve for \(x\): \(13x+26=3x-34\).

Answer 1

To solve the equation \( 13x + 26 = 3x - 34 \), we start by getting all terms involving \(x\) on one side and constants on the other side.

First, we'll subtract \(3x\) from both sides:

\[
13x - 3x + 26 = -34
\]

This simplifies to:

\[
10x + 26 = -34
\]

Next, we subtract \(26\) from both sides:

\[
10x = -34 - 26
\]

Simplifying the right side:

\[
10x = -60
\]

Now, we divide both sides by \(10\):

\[
x = \frac{-60}{10} = -6
\]

Thus, the solution for \(x\) is:

\[
\boxed{-6}
\]

To verify, substitute \(x = -6\) back into the original equation:

Calculating the left side:

\[
13(-6) + 26 = -78 + 26 = -52
\]

Calculating the right side:

\[
3(-6) - 34 = -18 - 34 = -52
\]

Both sides are equal, confirming that the solution \(x = -6\) is correct.