1. Solve the inequality $-2(x - 5) < 4$. Distribute to get $-2x + 10 < 4$. Subtract 10 from both sides: $-2x < -6$. Divide both sides by $-2$ and reverse inequality: $x > 3$. Check options: only option (c) $3$ satisfies $x > 3$? No, because $3$ is not greater than $3$. Actually $x > 3$, so options greater than 3. None of given options are greater than 3; however, check values: (a) 0 no, (b) 2 no, (c) 3 no, (d) 5 yes ($5>3$). So answer is (d) 5. 2. Solve $rac{4}{3}x + 5 < 17$. Subtract 5: $rac{4}{3}x < 12$. Multiply both sides by $rac{3}{4}$: $x < 9$. Check options less than 9: (a) 8 yes, (b) 12 no, (c) 9 no as it is not less than, (d) 16 no. Answer: (a) 8. 3. Solve $3x + 2 \\leq 5(x-4)$. Expand right: $3x + 2 \\leq 5x - 20$. Subtract $3x$: $2 \\leq 2x - 20$. Add 20: $22 \\leq 2x$. Divide both sides by 2: $11 \\leq x$ or $x \\geq 11$. Answer: (d) $x \\geq 11$. 4. Solve $3(2m-1) \\leq 4m +7$. Expand left: $6m - 3 \\leq 4m + 7$. Subtract $4m$: $2m - 3 \\leq 7$. Add 3: $2m \\leq 10$. Divide by 2: $m \\leq 5$. Answer: (c) $m \\leq 5$. 5. Interval notation for all real numbers $>2$ and $\\leq 20$ is $(2,20]$. Answer: (b) $(2,20]$. 6. Inequality $-2 \\leq x \\leq 3$ translates to $[-2,3]$ including endpoints. Answer: (d) $[-2,3]$. 7. Set {11,12} means integers between 11 and 12 inclusive? Given options: (a) $11 < x < 12$, no because $11$ and $12$ are not in. (b) $11 < x \\leq 12$, $x=12$ included but 11 excluded. (c) $10 < x \\leq 12$, $11$ and $12$ included, matches {11,12}. (d) $10 \\leq x < 12$, includes 10 and 11 but not 12. Answer: (c). 8. Integers in $[6,10)$ are $6,7,8,9$. Answer: (a). 9. Inequality $-3 < x \\leq 7$ corresponds to $(-3,7]$. Answer: (a). 10. Integers in $(-1,3]$ are $0,1,2,3$. Answer: (a).