To solve the equation \(3x + 2(x - 9) = 8x + x - 14\), we will first simplify each side of the equation step by step.
Starting with the left side:
- Distribute \(2\) in the term \(2(x - 9)\): \[ 3x + 2x - 18 \] Combining like terms: \[ 5x - 18 \]
Now the left side becomes: \[ 5x - 18 \]
Now for the right side:
- Combine like terms: \[ 8x + x - 14 = 9x - 14 \]
Now we have the simplified equation: \[ 5x - 18 = 9x - 14 \]
Next, we'll isolate \(x\) by getting all terms involving \(x\) on one side and the constant terms on the other:
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Subtract \(5x\) from both sides: \[ -18 = 9x - 5x - 14 \] This simplifies to: \[ -18 = 4x - 14 \]
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Add \(14\) to both sides: \[ -18 + 14 = 4x \] This simplifies to: \[ -4 = 4x \]
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Divide both sides by \(4\): \[ x = -1 \]
Thus, the solution to the equation is:
\[ \boxed{-1} \]
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