To solve the inequality \( x + 2 \frac{1}{2} < 8 \), we first convert \( 2 \frac{1}{2} \) into a fraction:
\[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \]
Now we can rewrite the inequality:
\[ x + \frac{5}{2} < 8 \]
Next, we will isolate \( x \) by subtracting \( \frac{5}{2} \) from both sides:
\[ x < 8 - \frac{5}{2} \]
To subtract \( \frac{5}{2} \) from 8, we need to express 8 as a fraction:
\[ 8 = \frac{16}{2} \]
Now we can perform the subtraction:
\[ x < \frac{16}{2} - \frac{5}{2} = \frac{16 - 5}{2} = \frac{11}{2} \]
Thus, the solution to the inequality with \( x \) coming first is:
\[ x < \frac{11}{2} \]
If you want to express it as a mixed number:
\[ x < 5 \frac{1}{2} \]
The final result is:
\[ x < \frac{11}{2} \] or \( x < 5 \frac{1}{2} \) in mixed fraction form.
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