To solve the equation \( 5(x + 3) - 7(x - 4) = 38 \), follow these steps:
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Distribute the numbers outside the parentheses: \[ 5(x + 3) = 5x + 15 \] \[ -7(x - 4) = -7x + 28 \]
So, the equation becomes: \[ 5x + 15 - 7x + 28 = 38 \]
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Combine like terms: \[ (5x - 7x) + (15 + 28) = 38 \] \[ -2x + 43 = 38 \]
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Isolate the variable by subtracting 43 from both sides: \[ -2x = 38 - 43 \] \[ -2x = -5 \]
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Divide both sides by -2: \[ x = \frac{-5}{-2} \] \[ x = \frac{5}{2} \]
So, the solution is: \[ x = \frac{5}{2} \]
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