1. The problem is to solve the equation $$|4x + 2| = 18$$ and find the values of $x$. 2. Recall that the absolute value equation $|A| = B$ means $A = B$ or $A = -B$ when $B \geq 0$. 3. Apply this rule to our equation: $$4x + 2 = 18 \quad \text{or} \quad 4x + 2 = -18$$ 4. Solve each equation separately. For $4x + 2 = 18$: $$4x = 18 - 2$$ $$4x = 16$$ $$x = \frac{16}{4}$$ $$x = 4$$ For $4x + 2 = -18$: $$4x = -18 - 2$$ $$4x = -20$$ $$x = \frac{-20}{4}$$ $$x = -5$$ 5. The solutions to the equation are $x = 4$ and $x = -5$. 6. These solutions correspond to the points marked on the number line at $-5$ and $4$ respectively. Final answer: $$x = 4 \text{ or } x = -5$$