To solve the equation \( 13x + 26 = 3x - 34 \), we will first rearrange the equation to isolate \( x \).
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Subtract \( 3x \) from both sides: \[ 13x - 3x + 26 = -34 \] \[ 10x + 26 = -34 \]
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Next, subtract 26 from both sides: \[ 10x + 26 - 26 = -34 - 26 \] \[ 10x = -60 \]
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Now divide both sides by 10: \[ x = \frac{-60}{10} \] \[ x = -6 \]
Thus, the solution is \( x = -6 \).
The correct answer is C. \( x = -6 \).