Question

1. X + ⅔ < 9, solve inequality..write as mixed number.

Answer 1

To solve the inequality \( X + \frac{2}{3} < 9 \), follow these steps:

1. Subtract \(\frac{2}{3}\) from both sides of the inequality:

\[
X < 9 - \frac{2}{3}
\]

2. To perform the subtraction, convert 9 into a fraction with a denominator of 3:

\[
9 = \frac{27}{3}
\]

3. Now the equation becomes:

\[
X < \frac{27}{3} - \frac{2}{3}
\]

4. Subtract the fractions:

\[
X < \frac{27 - 2}{3} = \frac{25}{3}
\]

5. To convert \(\frac{25}{3}\) into a mixed number, divide 25 by 3:

\[
25 \div 3 = 8 \quad \text{(the whole number part)}
\]
\[
25 - (3 \times 8) = 25 - 24 = 1 \quad \text{(the remainder)}
\]

Thus, \(\frac{25}{3} = 8 \frac{1}{3}\).

So the solution to the inequality \( X + \frac{2}{3} < 9 \) is:

\[
X < 8 \frac{1}{3}
\]