To solve the inequality \(x + 2 \frac{1}{2} < 8\), we first convert the mixed number \(2 \frac{1}{2}\) into an improper fraction.
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Convert \(2 \frac{1}{2}\): \[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \]
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Now substitute back into the inequality: \[ x + \frac{5}{2} < 8 \]
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To eliminate the fraction, we can subtract \(\frac{5}{2}\) from both sides: \[ x < 8 - \frac{5}{2} \]
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Convert \(8\) into a fraction: \[ 8 = \frac{16}{2} \] So now the inequality is: \[ x < \frac{16}{2} - \frac{5}{2} \]
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Now perform the subtraction: \[ x < \frac{16 - 5}{2} = \frac{11}{2} \]
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Thus, the solution is: \[ x < \frac{11}{2} \]
You can write your final answer as: \[ x < \frac{11}{2} \]
Or, if you prefer mixed numbers, you can also write: \[ x < 5 \frac{1}{2} \]
This is your final answer!
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