To solve the inequality \( x + 2 \frac{1}{2} < 8 \), we first convert \( 2 \frac{1}{2} \) into an improper fraction or a decimal.
Converting to an improper fraction: \[ 2 \frac{1}{2} = \frac{5}{2} \]
Now substituting this back into the inequality: \[ x + \frac{5}{2} < 8 \]
Next, we want to isolate \( x \). To do this, we subtract \( \frac{5}{2} \) from both sides: \[ x < 8 - \frac{5}{2} \]
To perform the subtraction, we convert 8 into a fraction with a denominator of 2: \[ 8 = \frac{16}{2} \]
Now we can subtract: \[ 8 - \frac{5}{2} = \frac{16}{2} - \frac{5}{2} = \frac{11}{2} \]
So the inequality becomes: \[ x < \frac{11}{2} \]
To write it in the standard form with \( x \) first: \[ x < \frac{11}{2} \]
Thus, the solution to the inequality is: \[ x < \frac{11}{2} \]
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