To solve the equation \(-15x + 24 + 16x = 3x - 24\), we will start by combining like terms on the left side.
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Combine the \(x\) terms on the left: \[ -15x + 16x = 1x \] Thus, the equation simplifies to: \[ 1x + 24 = 3x - 24 \]
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Now, we can rewrite the equation: \[ x + 24 = 3x - 24 \]
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Next, we want to isolate \(x\). Subtract \(x\) from both sides: \[ 24 = 2x - 24 \]
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Now, add 24 to both sides: \[ 24 + 24 = 2x \] \[ 48 = 2x \]
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Divide both sides by 2 to solve for \(x\): \[ x = \frac{48}{2} = 24 \]
So the solution is: \[ \boxed{24} \]