To solve the equation \( 9x + 20 + 2(3x - 4) = -2(4 - 6x) \), we can begin by simplifying both sides.
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Distribute the terms inside the parentheses: \[ 2(3x - 4) = 6x - 8 \] \[ -2(4 - 6x) = -8 + 12x \]
Substituting these back into the equation gives: \[ 9x + 20 + 6x - 8 = -8 + 12x \]
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Combine like terms: On the left side: \[ 9x + 6x + 20 - 8 = 15x + 12 \]
The equation now looks like: \[ 15x + 12 = -8 + 12x \]
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Rearranging the equation: Let's get all \( x \) terms on one side and constant terms on the other side. Subtract \( 12x \) from both sides: \[ 15x - 12x + 12 = -8 \] Simplifying gives: \[ 3x + 12 = -8 \]
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Isolate \( x \): Subtract \( 12 \) from both sides: \[ 3x = -8 - 12 \] \[ 3x = -20 \]
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Solve for \( x \): Divide by \( 3 \): \[ x = -\frac{20}{3} \]
Thus, the solution is: \[ \boxed{-\frac{20}{3}} \]