1. Solve the inequality: 2(x - 3) < 4 Distribute 2: 2x - 6 < 4 Add 6 to both sides: 2x < 10 Divide both sides by 2: x < 5 Answer: (c) x < 5 2. Solve the inequality: 3 - 2x ≤ 6 Subtract 3 from both sides: -2x ≤ 3 Divide by -2 and flip inequality: x ≥ -3/2 Answer: (a) x ≥ -3/2 3. Solve the inequality: 2(x - 4) - 3 > 2x - 1 Expand: 2x - 8 - 3 > 2x - 1 Simplify left: 2x - 11 > 2x - 1 Subtract 2x: -11 > -1, which is false No solutions Answer: (a) ∅ 4. Solve the inequality: 2(x - 4) + 11 > 2x - 1 Expand: 2x - 8 + 11 > 2x - 1 Simplify left: 2x + 3 > 2x - 1 Subtract 2x: 3 > -1, always true All real x satisfy Answer: (d) (-∞, ∞) 5. Interval [2, 5] means 2 ≤ x ≤ 5 Answer: (b) 2 ≤ x ≤ 5 6. Interval [-6, ∞) is all numbers from -6 (included) to infinity Graphically: solid dot at -6 with arrow to right Answer: (d) A number line with a solid dot at -6 and an arrow pointing right from -6 7. Solve compound inequality: -x + 3 ≤ 2x + 3 ≤ 9 Split and solve: First: -x + 3 ≤ 2x + 3 -> -x ≤ 2x -> -3x ≤ 0 -> x ≥ 0 Second: 2x + 3 ≤ 9 -> 2x ≤ 6 -> x ≤ 3 Combine: 0 ≤ x ≤ 3 Answer: (b) 0 ≤ x ≤ 3 8. Solve compound inequality: -4 ≤ 2x + 2 ≤ 10 Subtract 2: -6 ≤ 2x ≤ 8 Divide by 2: -3 ≤ x ≤ 4 Answer: (c) -3 ≤ x ≤ 4 9. Solve compound inequality: 4 ≤ -x + 3 ≤ 12 Break down: 4 ≤ -x + 3 -> 1 ≤ -x -> x ≤ -1 -x + 3 ≤ 12 -> -x ≤ 9 -> x ≥ -9 Combine inequalities: -9 ≤ x ≤ -1 Answer: (d) -9 ≤ x ≤ -1 26. Solve inequality: 7 - (2/3)x < x - 8 Rewrite: 7 + (-2/3)x < x - 8 Subtract 7: (-2/3)x < x - 15 Subtract x: (-2/3)x - x < -15 Combine: (-2/3 - 1)x < -15 (-5/3)x < -15 Multiply both sides by -3/5 (flip inequality): x > 9 Answer: (a) x > 9