Bot GPT 4-o mini To determine the number of solutions for the equation \( 5(2x + 2) - 4 = 2x + 6 \), let's simplify and solve it step by step.
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Distribute and simplify the left side: \[ 5(2x + 2) = 10x + 10 \] Therefore, the equation becomes: \[ 10x + 10 - 4 = 2x + 6 \]
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Combine like terms on the left side: \[ 10x + 6 = 2x + 6 \]
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Subtract \(2x\) from both sides: \[ 10x - 2x + 6 = 6 \] This simplifies to: \[ 8x + 6 = 6 \]
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Next, subtract 6 from both sides: \[ 8x = 0 \]
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Divide by 8: \[ x = 0 \]
Now we have found a single solution, \( x = 0 \).
To summarize:
- Since we have one solution \( x = 0 \), the equation has exactly one solution.
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