Question

What number could replace x to make a true statement?

Two-thirds less-than StartFraction x Over 8 EndFraction less-than StartFraction 7 Over 8 EndFraction
3
4
5
6

Answer 1

To solve the inequality \( \frac{2}{3} < \frac{x}{8} < \frac{7}{8} \), we will break it down into two parts.

### Step 1: Solve the left part \( \frac{2}{3} < \frac{x}{8} \)

Multiply both sides by 8 to eliminate the fraction:
\[
8 \cdot \frac{2}{3} < x
\]

Calculating \( 8 \cdot \frac{2}{3} \):
\[
\frac{16}{3} < x
\]

Calculating \( \frac{16}{3} \) numerically:
\[
\frac{16}{3} \approx 5.33
\]
This means \( x > 5.33 \).

### Step 2: Solve the right part \( \frac{x}{8} < \frac{7}{8} \)

Again, multiply both sides by 8:
\[
x < 7
\]

### Step 3: Combine the inequalities

We have the combined inequalities:
\[
5.33 < x < 7
\]

### Step 4: Evaluate the options

The provided options are: 3, 4, 5, 6.

- \(3\) is not greater than \(5.33\).
- \(4\) is not greater than \(5.33\).
- \(5\) is not greater than \(5.33\).
- \(6\) is greater than \(5.33\) and less than \(7\).

Thus, the only number that can replace \(x\) to make the statement true is:

\[
\boxed{6}
\]