To solve the equation \(3(2x + 2) - 4 = -2x + 10\), we will simplify and determine the value of \(x\).
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Start by distributing \(3\) on the left side: \[ 3(2x) + 3(2) - 4 = -2x + 10 \] This simplifies to: \[ 6x + 6 - 4 = -2x + 10 \] Which further simplifies to: \[ 6x + 2 = -2x + 10 \]
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Next, we will get all terms involving \(x\) on one side and constant terms on the other side:
- Add \(2x\) to both sides: \[ 6x + 2x + 2 = 10 \] Simplifying gives: \[ 8x + 2 = 10 \]
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Now subtract \(2\) from both sides: \[ 8x = 8 \]
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Finally, divide by \(8\): \[ x = 1 \]
We found one solution: \(x = 1\).
Conclusion: The equation has one solution: \(x = 1\).