Question: d)
-4(z - 12) = 42
1. **State the problem:** Solve the equation $$-4(z - 12) = 42$$ for the variable $$z$$.
2. **Use the distributive property:** Multiply $$-4$$ by each term inside the parentheses.
$$-4(z - 12) = -4 \times z + (-4) \times (-12) = -4z + 48$$
So the equation becomes:
$$-4z + 48 = 42$$
3. **Isolate the variable term:** Subtract $$48$$ from both sides.
$$-4z + 48 - 48 = 42 - 48$$
$$-4z = -6$$
4. **Divide both sides by $$-4$$ to solve for $$z$$:**
$$z = \frac{-6}{-4}$$
5. **Simplify the fraction:**
$$z = \frac{\cancel{-6}}{\cancel{-4}} \times \frac{1}{1} = \frac{6}{4}$$
6. **Reduce the fraction to simplest form:**
$$z = \frac{3}{2}$$
**Final answer:** $$z = \frac{3}{2}$$