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: \[ x < 9 \]