To solve the inequality \( x + 2 \frac{1}{2} < 8 \), we first convert \( 2 \frac{1}{2} \) to an improper fraction:
\[ 2 \frac{1}{2} = 2 \times 2 + 1 = 5/2. \]
Now we rewrite the inequality:
\[ x + \frac{5}{2} < 8. \]
Next, we subtract \( \frac{5}{2} \) from both sides of the inequality:
\[ x < 8 - \frac{5}{2}. \]
To perform the subtraction, we need to convert \( 8 \) into a fraction with a denominator of \( 2 \):
\[ 8 = \frac{16}{2}. \]
Now we can subtract:
\[ x < \frac{16}{2} - \frac{5}{2} = \frac{16 - 5}{2} = \frac{11}{2}. \]
So, we have:
\[ x < \frac{11}{2}. \]
To write the inequality with \( x \) coming first, we can rewrite it as:
\[ \frac{11}{2} > x. \]
Thus, the final inequality with \( x \) first is:
\[ x < \frac{11}{2}. \] or \[ x < 5.5. \]
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