Question

x - 2 wholes 1/3 < 2 wholes 1/6 solve the inequality

Answer 1

To solve the inequality \(x - 2 \frac{1}{3} < 2 \frac{1}{6}\), we first need to convert the mixed numbers into improper fractions.

1. Convert \(2 \frac{1}{3}\):
\[
2 \frac{1}{3} = 2 \times 3 + 1 = 6 + 1 = \frac{7}{3}
\]

2. Convert \(2 \frac{1}{6}\):
\[
2 \frac{1}{6} = 2 \times 6 + 1 = 12 + 1 = \frac{13}{6}
\]

Now, the inequality is:
\[
x - \frac{7}{3} < \frac{13}{6}
\]

Next, we want to isolate \(x\). We do this by adding \(\frac{7}{3}\) to both sides:
\[
x < \frac{13}{6} + \frac{7}{3}
\]

To add these fractions, we need a common denominator. The least common multiple of 6 and 3 is 6. We convert \(\frac{7}{3}\) to a fraction with a denominator of 6:
\[
\frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6}
\]

Now we can add:
\[
x < \frac{13}{6} + \frac{14}{6} = \frac{27}{6}
\]

We can simplify \(\frac{27}{6}\) to:
\[
\frac{27}{6} = \frac{9}{2}
\]

Thus, the solution to the inequality is:
\[
x < \frac{9}{2}
\]

Alternatively, in mixed number form, \(\frac{9}{2}\) is:
\[
\frac{9}{2} = 4 \frac{1}{2}
\]

So, the final answer is:
\[
x < 4 \frac{1}{2}
\]