Question

show a simple way of doing this inequaltiy
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 variable term**: Start by subtracting 12 from both sides.

\[
12 - \frac{2}{3}x - 12 > 6 - 12
\]

This simplifies to:

\[
-\frac{2}{3}x > -6
\]

2. **Eliminate the negative coefficient**: To make the coefficient of \( x \) positive, multiply both sides of the inequality by -1. Remember to flip the inequality sign when you do this.

\[
\frac{2}{3}x < 6
\]

3. **Solve for \( x \)**: To get \( x \) by itself, multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):

\[
x < 6 \cdot \frac{3}{2}
\]

Calculate \( 6 \cdot \frac{3}{2} \):

\[
6 \cdot \frac{3}{2} = \frac{18}{2} = 9
\]

4. **Final result**: Thus, the solution to the inequality is:

\[
x < 9
\]

This tells us that \( x \) can take any value less than 9.