Graph the solution set.
-$$\left| x ^ { 2 } + 9 \right| = | 6 x |$$
A) $\{ - 3,3 \}$
B) $\varnothing$
C) $\{ - 3 \}$
D) $\{ 3 \}$

Question

Quizplus · Accepted Answer

The equation $\left| x ^ { 2 } + 9 \right| = | 6 x |$ can be solved by considering the absolute value properties. We have two cases to consider due to the absolute values:1. $x^2 + 9 = 6x$ and 2. $x^2 + 9 = -6x$.For the first case, rearranging gives $x^2 - 6x + 9 = 0$, which factors to $(x-3)^2 = 0$, yielding $x = 3$.For the second case, rearranging gives $x^2 + 6x + 9 = 0$, which factors to $(x+3)^2 = 0$, yielding $x = -3$.Thus, the solution set is $\{-3, 3\}$.

Graph the Solution Set ∣x2+9∣=∣6x∣\left| x ^ { 2 } + 9 \right| = | 6 x |​x2+9​=∣6x∣

Graph the Solution Set $\left| x ^ { 2 } + 9 \right| = | 6 x |$