Solve the inequality graphically. -$\left( \frac { 1 } { 5 } \right) ^ { x } \left( \frac { 1 } { 3 } \right) ^ { x }$ A) $x 0$ C) $x 1$ D) $x

Question

Solve the inequality graphically. -$\left( \frac { 1 } { 5 } \right) ^ { x } > \left( \frac { 1 } { 3 } \right) ^ { x }$ A) $x < 1$ B) $x > 0$ C) $x > 1$ D) $x < 0$

Quizplus · Accepted Answer

The inequality $\left( \frac { 1 } { 5 } \right) ^ { x } > \left( \frac { 1 } { 3 } \right) ^ { x }$ can be solved graphically by plotting the two functions $y = \left( \frac { 1 } { 5 } \right) ^ { x }$ and $y = \left( \frac { 1 } { 3 } \right) ^ { x }$. Since both bases are fractions less than 1, their graphs will be decreasing. The inequality is true where the graph of $\left( \frac { 1 } { 5 } \right) ^ { x }$ is above the graph of $\left( \frac { 1 } { 3 } \right) ^ { x }$. This occurs when $x < 0$, because as x decreases (becomes more negative), the value of $\left( \frac { 1 } { 5 } \right) ^ { x }$ becomes larger than the value of $\left( \frac { 1 } { 3 } \right) ^ { x }$ due to the nature of exponential functions with bases between 0 and 1.

Solve the Inequality Graphically (15)x>(13)x\left( \frac { 1 } { 5 } \right) ^ { x } > \left( \frac { 1 } { 3 } \right) ^ { x }(51​)x>(31​)x

Solve the Inequality Graphically $\left( \frac { 1 } { 5 } \right) ^ { x } > \left( \frac { 1 } { 3 } \right) ^ { x }$