To determine the number of solutions for the equation \(5(2x + 2) - 4 = 2x + 6\), we will simplify and solve it step by step.
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Start by simplifying the left side: \[ 5(2x + 2) - 4 = 10x + 10 - 4 = 10x + 6 \] So, the equation now is: \[ 10x + 6 = 2x + 6 \]
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Next, let's isolate the variable \(x\) by subtracting \(2x\) from both sides: \[ 10x - 2x + 6 = 6 \] This simplifies to: \[ 8x + 6 = 6 \]
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Subtract 6 from both sides: \[ 8x = 0 \]
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Finally, divide by 8: \[ x = 0 \]
Now let's consider the types of solutions:
- If \(x = 0\) is the only solution, the equation has one solution.
To summarize, the equation \(5(2x + 2) - 4 = 2x + 6\) has one solution, \(x = 0\).