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.
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