To solve the equation \(5(2x+2)−4=2x+6\), we'll first simplify both sides.
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Distribute the \(5\) on the left side: \[ 5(2x) + 5(2) - 4 = 10x + 10 - 4 = 10x + 6 \] So the left side becomes: \[ 10x + 6 \]
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Now, rewrite the equation: \[ 10x + 6 = 2x + 6 \]
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Next, we'll move \(2x\) from the right side to the left side by subtracting \(2x\) from both sides: \[ 10x - 2x + 6 = 6 \] This simplifies to: \[ 8x + 6 = 6 \]
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Now, subtract \(6\) from both sides: \[ 8x + 6 - 6 = 6 - 6 \] This simplifies to: \[ 8x = 0 \]
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Now, divide both sides by \(8\): \[ x = 0 \]
Now we interpret the solution. Since we've found a single value of \(x\), the equation has one solution.
Therefore, the answer is: The equation has one solution: x = 0.