Let's go through your steps to check your work:
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Starting equation: \[ 2(x - 2) + 5x = 24 \]
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Step 1: Distributing the 2: \[ 2x - 4 + 5x = 24 \]
- This step is correct.
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Step 2: Combining like terms: \[ 2x + 5x - 4 = 24 \implies 7x - 4 = 24 \]
- Here, you made an error. It should be \(7x - 4 = 24\), not \(10x - 4 = 24\).
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Step 3: Adding 4 to both sides: \[ 7x - 4 + 4 = 24 + 4 \implies 7x = 28 \]
- This part is fine, but remember you should have \(7x\) instead of \(10x\).
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Step 4: Dividing both sides by 7: \[ \frac{7x}{7} = \frac{28}{7} \implies x = 4 \]
- You were planning to divide by 10, but it should be by 7, giving you \(x = 4\).
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Final Answer: \[ x = 4 \]
So the correct solution is \(x = 4\).
Your initial setup was good, but there was an error in combining like terms. The correct value of \(x\) is 4, not 2.8.
2 answers