1. The problem is to solve the equation $$|6x| = 36$$ for all values of $x$. 2. Recall that the absolute value equation $|A| = B$ means $A = B$ or $A = -B$ when $B \geq 0$. 3. Here, $A = 6x$ and $B = 36$, so we set up two equations: $$6x = 36$$ $$6x = -36$$ 4. Solve each equation for $x$: For $6x = 36$: $$x = \frac{36}{6} = 6$$ For $6x = -36$: $$x = \frac{-36}{6} = -6$$ 5. Therefore, the solutions are $$x = 6$$ and $$x = -6$$. These are the simplest forms of $x$ that satisfy the original equation.