Question

x + 2 wholes 1/2 < 2 wholes 1/2 solve the inequality

Answer 1

To solve the inequality \( x + 2 \frac{1}{2} < 2 \frac{1}{2} \), first convert the mixed numbers into improper fractions or decimals for easier manipulation.

1. Convert \( 2 \frac{1}{2} \) to an improper fraction:

\[
2 \frac{1}{2} = 2 \times 2 + 1 = 5 \quad \text{(or as an improper fraction: } \frac{5}{2})
\]

2. Now rewrite the inequality:

\[
x + 2 \frac{1}{2} < 5
\]

Converting \( 2 \frac{1}{2} \) gives:

\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{5}{2}
\]

So the inequality is:

\[
x + \frac{5}{2} < 5
\]

3. Now eliminate the fraction by subtracting \( \frac{5}{2} \) from both sides:

\[
x < 5 - \frac{5}{2}
\]

Converting \( 5 \) to a fraction with a denominator of \( 2 \):

\[
5 = \frac{10}{2}
\]

Now perform the subtraction:

\[
x < \frac{10}{2} - \frac{5}{2} = \frac{5}{2}
\]

4. Therefore, the solution to the inequality is:

\[
x < \frac{5}{2} \quad \text{or} \quad x < 2 \frac{1}{2}
\]

So, in conclusion, the solution is:

\[
x < 2 \frac{1}{2}
\]