Question

easy way ti solve 12 - 2/3x is greater than 6

Answer 1

To solve the inequality \( 12 - \frac{2}{3}x > 6 \), follow these steps:

1. **Isolate the term with \( x \)**:
\[
12 - 6 > \frac{2}{3}x
\]
Simplifying the left side gives:
\[
6 > \frac{2}{3}x
\]

2. **Rearranging the inequality**:
Multiply both sides by \(-1\) (note that this reverses the inequality):
\[
-6 < -\frac{2}{3}x
\]

3. **Multiply both sides by \(-\frac{3}{2}\)** (again, flipping the inequality):
\[
-6 \cdot -\frac{3}{2} > x
\]
Simplifying this gives:
\[
9 > x
\]
or
\[
x < 9
\]

Thus, the solution to the inequality \( 12 - \frac{2}{3}x > 6 \) is:
\[
x < 9
\]