Checkpoint: Exponential Inequalities Solution

Solve.

$125^{4 x - 4} \geq 625^{3 - x}$

  $\begin{array}{rcl} 125 = 5^{3} 625 = 5^{4} \\ 5^{3 (4 x - 4)} & \geq & 5^{4 (3 - x)} \\ 3 (4 x - 4) & \geq & 4 (3 - x) \\ 12 x - 12 & \geq & 12 - 4 x \\ 16 x & \geq & 24 \\ x & \geq & 1.5 \end{array}$

Note

Q: What causes the direction of the inequality symbol to change?

A: Multiplying or dividing both sides by a negative number. 

Your method of solving determines if you must divide by a negative number.