Question

Solve the linear inequality 1/3x−1>2
.(1 point)
Responses

x<9
x less than 9

x>9
x greater than 9

x<7
x less than 7

x>7
x greater than 7

Answer 1

To solve the inequality \( \frac{1}{3}x - 1 > 2 \), follow these steps:

1. **Add 1 to both sides**:
\[
\frac{1}{3}x - 1 + 1 > 2 + 1
\]
Simplifying this gives:
\[
\frac{1}{3}x > 3
\]

2. **Multiply both sides by 3** (to eliminate the fraction):
\[
3 \cdot \frac{1}{3}x > 3 \cdot 3
\]
This simplifies to:
\[
x > 9
\]

Thus, the solution to the inequality is \( x > 9 \).

The correct response is:
**x > 9** (x greater than 9).