1. **State the problem:** Solve the equation $f(x) = 5$ where $f(x) = |3x - 4|$. 2. **Recall the definition of absolute value:** For any real number $a$, $|a| = b$ means $a = b$ or $a = -b$ where $b \geq 0$. 3. **Apply this to the equation:** $$|3x - 4| = 5$$ This implies two cases: Case 1: $$3x - 4 = 5$$ Case 2: $$3x - 4 = -5$$ 4. **Solve Case 1:** $$3x - 4 = 5$$ Add 4 to both sides: $$3x = 5 + 4 = 9$$ Divide both sides by 3: $$x = \frac{9}{3} = 3$$ 5. **Solve Case 2:** $$3x - 4 = -5$$ Add 4 to both sides: $$3x = -5 + 4 = -1$$ Divide both sides by 3: $$x = \frac{-1}{3}$$ 6. **Final solutions:** $$x = 3 \quad \text{or} \quad x = -\frac{1}{3}$$ 7. **Explain why $f$ is not injective:** A function is injective if each output corresponds to exactly one input. Here, $f(3) = |3(3) - 4| = |9 - 4| = 5$ and $f(-\frac{1}{3}) = |3(-\frac{1}{3}) - 4| = |-1 - 4| = 5$. Since two different inputs give the same output, $f$ is not injective.