Solve each inequality. Then graph the solution on a number line. \( \begin{array}{ll}\text { 16. }-3(7 n+3)<6 n & \text { 17. } 21 \geq 3(a-7)+9 \\ \text { 18. } 2 y+4>2(3+y) & \text { 19. } 3(2-b)<10-3(b-6) \\ \text { 20. } 7+t \leq 2(t+3)+2 & \text { 21. } 8 a+2(1-5 a) \leq 20\end{array} \)

We will solve each inequality step‐by‐step and then describe how to graph the solution on a number line. ───────────────────────────── 16. –3(7n + 3) < 6n 1. Distribute –3:   –21n – 9 < 6n 2. Add 21n to both sides:   –9 < 27n 3. Divide both sides by 27 (positive so the inequality sign remains the same):   n > –9/27 4. Simplify:   n > –1/3 Graph: On a number line, put an open circle at –1/3 and shade everything to the right.   Solution: n > –1/3 ───────────────────────────── 17. 21 ≥ 3(a – 7) + 9 1. Distribute 3:   21 ≥ 3a – 21 + 9 2. Combine like terms on the right:   21 ≥ 3a – 12 3. Add 12 to both sides:   33 ≥ 3a  or  3a ≤ 33 4. Divide both sides by 3:   a ≤ 11 Graph: On a number line, place a closed circle at 11 and shade everything to the left.   Solution: a ≤ 11 ───────────────────────────── 18. 2y + 4 > 2(3 + y) 1. Distribute 2 on the right:   2y + 4 > 6 + 2y 2. Subtract 2y from both sides:   4 > 6 This inequality is false (4 is never greater than 6) regardless of y. Graph: The number line will have no solution shaded.   Solution: No solution (empty set) ───────────────────────────── 19. 3(2 – b) < 10 – 3(b – 6) 1. Distribute on the left:   6 – 3b < 10 – 3(b – 6) 2. Expand the right side:   6 – 3b < 10 – 3b + 18 3. Simplify the right side:   6 – 3b < 28 – 3b 4. Add 3b to both sides:   6 < 28 Since 6 < 28 is always true, the inequality holds for every value of b. Graph: The entire real number line is shaded.   Solution: All real numbers (-∞, ∞) ───────────────────────────── 20. 7 + t ≤ 2(t + 3) + 2 1. Expand the right side:   7 + t ≤ 2t + 6 + 2 2. Simplify the right side:   7 + t ≤ 2t + 8 3. Subtract t from both sides:   7 ≤ t + 8 4. Subtract 8 from both sides:   -1 ≤ t  or  t ≥ -1 Graph: Place a closed circle at -1 and shade to the right.   Solution: t ≥ -1 ───────────────────────────── 21. 8a + 2(1 – 5a) ≤ 20 1. Distribute 2:   8a + 2 – 10a ≤ 20 2. Combine like terms:   -2a + 2 ≤ 20 3. Subtract 2 from both sides:   -2a ≤ 18 4. Divide both sides by –2 (note: reverse the inequality sign when dividing by a negative):   a ≥ -9 Graph: Place a closed circle at -9 and shade to the right.   Solution: a ≥ -9 ───────────────────────────── Summary of Solutions and Graph Descriptions: 16. n > –1/3   Graph: open circle at –1/3; shade to the right. 17. a ≤ 11   Graph: closed circle at 11; shade to the left. 18. No solution   Graph: no points shaded. 19. All real numbers (-∞, ∞)   Graph: entire number line shaded. 20. t ≥ -1   Graph: closed circle at -1; shade to the right. 21. a ≥ -9   Graph: closed circle at -9; shade to the right. Each solution is now solved and the graphing instructions provided as described above.