Question: D 2(2m - n) 3(2m + n) 16 Simplify 3/7b(14a - 21b) - a/2b. A 11a + 18b 2b B 11a - 18b 2b C 12a - 17b 2b D 13a - 18b 2b top-right: a multiple-choice algebra simplification problem is shown, with the expression 3/7b(14a - 21b) - a/2b and answer options A, B, C, D arranged vertically.User: Help. Form 2 maths.
1. **State the problem:** Simplify the expression $$\frac{3}{7b}(14a - 21b) - \frac{a}{2b}$$ and match it to one of the given options.
2. **Recall the distributive property:** $$k(x - y) = kx - ky$$ and rules for fractions.
3. **Distribute $$\frac{3}{7b}$$ over $$14a - 21b$$:**
$$\frac{3}{7b} \times 14a - \frac{3}{7b} \times 21b$$
4. **Calculate each term:**
$$\frac{3 \times 14a}{7b} - \frac{3 \times 21b}{7b} = \frac{42a}{7b} - \frac{63b}{7b}$$
5. **Simplify each fraction:**
$$\frac{42a}{7b} = \frac{\cancel{7}6a}{\cancel{7}b} = \frac{6a}{b}$$
$$\frac{63b}{7b} = \frac{\cancel{7}9\cancel{b}}{\cancel{7}\cancel{b}} = 9$$
6. **Rewrite the expression:**
$$\frac{6a}{b} - 9 - \frac{a}{2b}$$
7. **Combine the fractional terms $$\frac{6a}{b}$$ and $$-\frac{a}{2b}$$:**
Find common denominator $$2b$$:
$$\frac{6a}{b} = \frac{6a \times 2}{b \times 2} = \frac{12a}{2b}$$
So,
$$\frac{12a}{2b} - \frac{a}{2b} = \frac{12a - a}{2b} = \frac{11a}{2b}$$
8. **Rewrite the expression including the constant term:**
$$\frac{11a}{2b} - 9$$
9. **Express $$9$$ with denominator $$2b$$ to combine:**
$$9 = \frac{18b}{2b}$$
10. **Final subtraction:**
$$\frac{11a}{2b} - \frac{18b}{2b} = \frac{11a - 18b}{2b}$$
11. **Match with options:** This matches option B: $$\frac{11a - 18b}{2b}$$.
**Final answer:** Option B.