Questions: x / -3 > 3 / 2

Solution Steps

To solve the inequality \(\frac{x}{-3} > \frac{3}{2}\), we need to isolate \(x\). We can do this by multiplying both sides of the inequality by \(-3\). Remember that when multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed.

1. Multiply both sides of the inequality by \(-3\).
2. Reverse the inequality sign.
3. Simplify the resulting expression to find the value of \(x\).

Given the inequality: \[ \frac{x}{-3} > \frac{3}{2} \] we multiply both sides by \(-3\) to isolate \(x\). Remember to reverse the inequality sign when multiplying by a negative number: \[ x < \left(\frac{3}{2}\right) \times (-3) \]

Simplify the right-hand side of the inequality: \[ x < \frac{3 \times (-3)}{2} = \frac{-9}{2} = -4.5 \]

Final Answer