To solve the equation \(2 (3x - 8) = 2 (7x + 2)\), we can start by simplifying both sides.
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Distribute the 2 on both sides: \[ 2 \cdot (3x - 8) = 6x - 16 \] \[ 2 \cdot (7x + 2) = 14x + 4 \]
So, the equation now looks like this: \[ 6x - 16 = 14x + 4 \]
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Next, we want to isolate \(x\). Let's start by getting all terms involving \(x\) on one side and constant terms on the other side. We can subtract \(6x\) from both sides: \[ -16 = 14x - 6x + 4 \] This simplifies to: \[ -16 = 8x + 4 \]
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Now, subtract 4 from both sides to isolate the term with \(x\): \[ -16 - 4 = 8x \] Which gives us: \[ -20 = 8x \]
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Finally, divide both sides by 8 to solve for \(x\): \[ x = \frac{-20}{8} = \frac{-5}{2} \]
Thus, the value of \(x\) that makes the original equation true is: \[ \boxed{-\frac{5}{2}} \]