1. Solve each inequality in section 2 step-by-step. (a) Solve $5x - 6 < 29$: Add 6 to both sides: $5x < 35$ Divide both sides by 5: $x < 7$ (b) Solve $7x + 2 \geq -19$: Subtract 2: $7x \geq -21$ Divide by 7: $x \geq -3$ (c) Solve $5x - 8 \leq 12$: Add 8: $5x \leq 20$ Divide by 5: $x \leq 4$ (d) Solve $6x - 3 \geq 1$: Add 3: $6x \geq 4$ Divide by 6: $x \geq \frac{2}{3}$ (e) Solve $5x + 7 < 11$: Subtract 7: $5x < 4$ Divide by 5: $x < \frac{4}{5}$ (f) Solve $7x - 8 > -2$: Add 8: $7x > 6$ Divide by 7: $x > \frac{6}{7}$ (g) Solve $4 - 2x \geq -8$: Subtract 4: $-2x \geq -12$ Divide by -2 (reverse inequality): $x \leq 6$ (h) Solve $5 - 6x < -7$: Subtract 5: $-6x < -12$ Divide by -6 (reverse inequality): $x > 2$ (i) Solve $4(2 - x) \geq -8$: Expand: $8 - 4x \geq -8$ Subtract 8: $-4x \geq -16$ Divide by -4 (reverse inequality): $x \leq 4$ (j) Solve $7 + 4x \geq 19$: Subtract 7: $4x \geq 12$ Divide by 4: $x \geq 3$ (k) Solve $6 - 5x > -10$: Subtract 6: $-5x > -16$ Divide by -5 (reverse inequality): $x < \frac{16}{5}$ (l) Solve $\frac{3x - 4}{2} \geq 3$: Multiply both sides by 2: $3x - 4 \geq 6$ Add 4: $3x \geq 10$ Divide by 3: $x \geq \frac{10}{3}$ 2. Solve each compound inequality in section 3. (a) $5 < 3x + 2 \leq 11$ Subtract 2: $3 < 3x \leq 9$ Divide by 3: $1 < x \leq 3$ (b) $3 \leq 4x - 5 < 15$ Add 5: $8 \leq 4x < 20$ Divide by 4: $2 \leq x < 5$ (c) $11 \leq 4x + 7 < 27$ Subtract 7: $4 \leq 4x < 20$ Divide by 4: $1 \leq x < 5$ (d) $5 < 6x - 7 < 29$ Add 7: $12 < 6x < 36$ Divide by 6: $2 < x < 6$ (e) $-24 \leq 3x - 9 \leq -14$ Add 9: $-15 \leq 3x \leq -5$ Divide by 3: $-5 \leq x \leq -\frac{5}{3}$ (f) $-3 \leq 4x + 5 < 17$ Subtract 5: $-8 \leq 4x < 12$ Divide by 4: $-2 \leq x < 3$ Each solution can be illustrated on a number line with appropriate open or closed endpoints depending on strict or inclusive inequalities. Final answers: 2(a) $x < 7$ 2(b) $x \geq -3$ 2(c) $x \leq 4$ 2(d) $x \geq \frac{2}{3}$ 2(e) $x < \frac{4}{5}$ 2(f) $x > \frac{6}{7}$ 2(g) $x \leq 6$ 2(h) $x > 2$ 2(i) $x \leq 4$ 2(j) $x \geq 3$ 2(k) $x < \frac{16}{5}$ 2(l) $x \geq \frac{10}{3}$ 3(a) $1 < x \leq 3$ 3(b) $2 \leq x < 5$ 3(c) $1 \leq x < 5$ 3(d) $2 < x < 6$ 3(e) $-5 \leq x \leq -\frac{5}{3}$ 3(f) $-2 \leq x < 3$