Absolute Value Equation 0B71Ed

1. **State the problem:** Solve the equation $$|8m + 2| + 4 = 13$$ for the variable $$m$$. 2. **Isolate the absolute value:** Subtract 4 from both sides: $$|8m + 2| + 4 - 4 = 13 - 4$$ $$|8m + 2| = 9$$ 3. **Definition of absolute value:** For $$|x| = a$$ where $$a > 0$$, the solutions are $$x = a$$ or $$x = -a$$. Apply this to our equation: $$8m + 2 = 9 \quad \text{or} \quad 8m + 2 = -9$$ 4. **Solve each equation:** - For $$8m + 2 = 9$$: $$8m = 9 - 2$$ $$8m = 7$$ $$m = \frac{7}{8}$$ - For $$8m + 2 = -9$$: $$8m = -9 - 2$$ $$8m = -11$$ $$m = \frac{-11}{8}$$ 5. **Final answer:** The solutions are $$m = \frac{7}{8}$$ and $$m = \frac{-11}{8}$$. These correspond to option D.