solve (-(6)^{x - 1}+5 = (\frac{2}{3})^{2 - x}) by graphing. round to the nearest tenth.

Explanation:

Step1: Define two functions

Let $y_1 = -(6)^{x - 1}+5$ and $y_2=\left(\frac{2}{3}\right)^{2 - x}$.

Step2: Use a graphing - utility

Graph the two functions $y_1$ and $y_2$ on the same coordinate plane. The $x$ - value of the intersection point of the two graphs is the solution of the equation $-(6)^{x - 1}+5=\left(\frac{2}{3}\right)^{2 - x}$.

Step3: Find the intersection point

By using a graphing calculator or an online graphing tool, we find the intersection point. After rounding to the nearest tenth, we get the value of $x$.

Answer:

$x\approx2.4$