Solve the inequality graphically. -$\left( \frac { 1 } { 8 } \right) ^ { x } 0$ D) $x

Question

Solve the inequality graphically. -$\left( \frac { 1 } { 8 } \right) ^ { x } < \left( \frac { 1 } { 7 } \right) ^ { x }$ A) x < 0 B) $x > 1$ C) $x > 0$ D) $x < 1$

Quizplus · Accepted Answer

The inequality $\left( \frac { 1 } { 8 } \right) ^ { x } < \left( \frac { 1 } { 7 } \right) ^ { x }$ can be solved by recognizing that as $x$ increases, $\left( \frac { 1 } { 8 } \right) ^ { x }$ decreases more rapidly than $\left( \frac { 1 } { 7 } \right) ^ { x }$ because 1/8 is smaller than 1/7. Therefore, for $x > 0$, the left side of the inequality becomes smaller than the right side, making the inequality true.

Solve the Inequality Graphically (18)x<(17)x\left( \frac { 1 } { 8 } \right) ^ { x } < \left( \frac { 1 } { 7 } \right) ^ { x }(81​)x<(71​)x

Solve the Inequality Graphically $\left( \frac { 1 } { 8 } \right) ^ { x } < \left( \frac { 1 } { 7 } \right) ^ { x }$