Let's solve the equation correctly step by step.
The original equation is:
\[ 3x + 2x - 6 = 24 \]
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First, combine like terms on the left side:
\[ (3x + 2x) - 6 = 24 \] \[ 5x - 6 = 24 \]
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Next, add 6 to both sides to isolate the term with \(x\):
\[ 5x - 6 + 6 = 24 + 6 \] \[ 5x = 30 \]
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Now, divide both sides by 5 to solve for \(x\):
\[ x = \frac{30}{5} \] \[ x = 6 \]
So the correct solution is \(x = 6\).
Explanation of the Error:
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The first error occurs in the step where \(-2x - 2x\) was performed. It appears the equations were either incorrectly manipulated or miswritten.
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The subsequent step where \(x - 6 = 24\) was written is incorrect; it seems to have dropped some terms and made an arbitrary simplification that did not follow the rules of algebra.
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The final calculation mistakenly suggested adding 6 to both sides to get \(x = 30\) instead of recognizing that \(5x = 30\) must be divided by 5 to find \(x\).
The proper steps consistently follow arithmetic operations, and the use of parentheses to ensure each step is clear and accurate would help avoid such errors.
1 answer