To solve the equation \( 20x - 5(6x + 15) = -45 \), we will first simplify the left side.
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Distribute the \(-5\) through the parentheses: \[ 20x - 5(6x) - 5(15) = -45 \] which simplifies to: \[ 20x - 30x - 75 = -45 \]
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Combine like terms: \[ (20x - 30x) - 75 = -45 \] This simplifies to: \[ -10x - 75 = -45 \]
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To isolate the term involving \(x\), add \(75\) to both sides: \[ -10x - 75 + 75 = -45 + 75 \] Simplifying gives: \[ -10x = 30 \]
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Now, divide both sides by \(-10\): \[ x = \frac{30}{-10} \] This results in: \[ x = -3 \]
Thus, the solution for \(x\) is \(\boxed{-3}\).