12 - 2/3x greater than 6

Answer 1

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

1. Subtract 12 from both sides:

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

   Simplify:

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

2. Multiply both sides by \(-\frac{3}{2}\). Remember that when you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign:

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

   Calculating the right side:

   \[ x < 9 \]

So, the solution to the inequality \( 12 - \frac{2}{3}x > 6 \) is:

\[ x < 9 \]