Chapter 8.2, Problem 43HP

To determine

To find: The correct method between Beth method and Liz method.

Answer to Problem 43HP

Beth’s method is correct. Liz makes a mistake with the exponential property.

Explanation of Solution

Given information: The given information isBeth and Liz are solving the inequality $6^{x-3}>{36}^{-x-1}$.

Consider the inequality $6^{x-3}>{36}^{-x-1}$ . On solving it becomes $6^{x-3}>6^{-2x-1}$.

Solve the inequality

  $\begin{array}{c}x-3>-2x-2\\ x+2x>-2+3\\ 3x>1\\ x>\frac{1}{3}\end{array}$

Therefore, The Beth’s method is correct. Liz makes a mistake with the exponential property.