To solve the inequality \( x + 2 \frac{1}{2} < 8 \), we first convert \( 2 \frac{1}{2} \) into an improper fraction or a decimal.
\( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{5}{2} \) or \( 2.5 \).
Now we rewrite the inequality:
\[ x + \frac{5}{2} < 8 \]
Next, we subtract \( \frac{5}{2} \) from both sides:
\[ x < 8 - \frac{5}{2} \]
To subtract \( \frac{5}{2} \) from 8, we need a common denominator. Convert 8 to a fraction:
\[ 8 = \frac{16}{2} \]
Now perform the subtraction:
\[ x < \frac{16}{2} - \frac{5}{2} = \frac{16 - 5}{2} = \frac{11}{2} \]
Thus, the inequality can be written as:
\[ x < \frac{11}{2} \]
Finally, we can express it with \( x \) coming first:
\[ x < 5.5 \]
Therefore, the solution to the inequality is:
\[ x < \frac{11}{2} \] or \( x < 5.5 \).
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