To solve the equation \( 5(2x+2) - 4 = 2x + 6 \), let's first simplify it step by step.
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Distribute the 5 on the left side: \[ 5(2x) + 5(2) - 4 = 2x + 6 \] Which simplifies to: \[ 10x + 10 - 4 = 2x + 6 \] Or: \[ 10x + 6 = 2x + 6 \]
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Next, isolate the terms involving \( x \) on one side and constants on the other: Subtract \( 2x \) from both sides: \[ 10x - 2x + 6 = 6 \] This simplifies to: \[ 8x + 6 = 6 \]
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Now, subtract 6 from both sides: \[ 8x = 6 - 6 \] Which gives: \[ 8x = 0 \]
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Finally, divide by 8: \[ x = 0 \]
Now, let's interpret the solution. Since we found a single value for \( x \), that means the equation has one solution.
The correct response is: The equation has one solution: x=0.