1. **Problem:** Find which value of $x$ satisfies the equation $2x^2 + 5x = 7$. **Step:** Substitute each option into the equation and check. i) $x=1$: $2(1)^2 + 5(1) = 2 + 5 = 7$ ✓ satisfies. ii) $x=-2$: $2(-2)^2 + 5(-2) = 2(4) - 10 = 8 - 10 = -2$ ✗ does not satisfy. iii) $x=5$: $2(5)^2 + 5(5) = 2(25) + 25 = 50 + 25 = 75$ ✗ does not satisfy. iv) $x=0$: $2(0)^2 + 5(0) = 0$ ✗ does not satisfy. 2. **Problem:** Find which value of $u$ satisfies $5u + 1 = -4$. Substitute each option: i) $u=3$: $5(3) + 1 = 15 + 1 = 16$ ✗ ii) $u=7$: $5(7) + 1 = 35 + 1 = 36$ ✗ iii) $u=\frac{1}{5}$: $5(\frac{1}{5}) + 1 = 1 + 1 = 2$ ✗ iv) $u=-1$: $5(-1) + 1 = -5 + 1 = -4$ ✓ satisfies. 3. **Problem:** Find which value of $v$ satisfies $\frac{v}{2} - 2 = 1$. Substitute each option: i) $v=2$: $\frac{2}{2} - 2 = 1 - 2 = -1$ ✗ ii) $v=6$: $\frac{6}{2} - 2 = 3 - 2 = 1$ ✓ satisfies. iii) $v=10$: $\frac{10}{2} - 2 = 5 - 2 = 3$ ✗ iv) $v=30$: $\frac{30}{2} - 2 = 15 - 2 = 13$ ✗ 4. **Problem:** Find which value of $m$ satisfies $3m - 5 = 10$. Substitute each option: i) $m=-1$: $3(-1) - 5 = -3 - 5 = -8$ ✗ ii) $m=0$: $3(0) - 5 = 0 - 5 = -5$ ✗ iii) $m=-3$: $3(-3) - 5 = -9 - 5 = -14$ ✗ iv) $m=5$: $3(5) - 5 = 15 - 5 = 10$ ✓ satisfies. --- Part B: 1. **Problem:** Which equation is true at $s=5$? i) $s + 2 = 7$: $5 + 2 = 7$ ✓ true. ii) $s - 3 = 12$: $5 - 3 = 2$ ✗ false. iii) $2s + 5 = 23$: $2(5) + 5 = 10 + 5 = 15$ ✗ false. iv) $\frac{s}{5} - 1 = 8$: $\frac{5}{5} - 1 = 1 - 1 = 0$ ✗ false. 2. **Problem:** Which equation is true at $r = -1$? i) $r^2 + 2r = 3$: $(-1)^2 + 2(-1) = 1 - 2 = -1$ ✗ false. ii) $\frac{r}{5} + 5 = -8$: $\frac{-1}{5} + 5 = -0.2 + 5 = 4.8$ ✗ false. iii) $(r - 1)(2r + 1) = 2$: $(-1 - 1)(2(-1) + 1) = (-2)(-2 + 1) = (-2)(-1) = 2$ ✓ true. iv) $r^2 + 3r = -9$: $1 + (-3) = -2$ ✗ false. 3. **Problem:** Which equation is true at $a=2$? i) $(a + 1)(5a - 3) = 2$: $(2 + 1)(5(2) - 3) = 3(10 - 3) = 3(7) = 21$ ✗ false. ii) $a^2 + 7a + 2 = 37$: $4 + 14 + 2 = 20$ ✗ false. iii) $\frac{2}{a} + 1 = -7$: $\frac{2}{2} + 1 = 1 + 1 = 2$ ✗ false. iv) $\frac{3a - 2}{a} = 2$: $\frac{3(2) - 2}{2} = \frac{6 - 2}{2} = \frac{4}{2} = 2$ ✓ true. **Final answers:** Part A: 1) i, 2) iv, 3) ii, 4) iv Part B: 1) i, 2) iii, 3) iv