1. Solve $0.2x = 7$. Divide both sides by $0.2$: $$x = \frac{7}{0.2} = 35$$ 2. Solve $5x - 3 = 9$. Add 3 to both sides: $$5x = 12$$ Divide by 5: $$x = \frac{12}{5} = 2.4$$ 3. Solve $2(p - 1) - 3(p - 4) = 4p$: Expand: $$2p - 2 - 3p + 12 = 4p$$ Simplify: $$-p + 10 = 4p$$ Add $p$ to both sides: $$10 = 5p$$ Divide by 5: $$p = 2$$ 4. Solve $(t + 1)(t + 2) = 0$ by zero product property: $$t + 1 = 0 \Rightarrow t = -1$$ $$t + 2 = 0 \Rightarrow t = -2$$ 5. Solve quadratic $x^2 - 2x - 3 = 0$ by factoring: $$(x-3)(x+1) = 0$$ Set each factor to zero: $$x=3 \text{ or } x=-1$$ 6. Solve inequality $5x - 11 \leq 9$: Add 11: $$5x \leq 20$$ Divide by 5: $$x \leq 4$$ 7. Solve inequality $4s - 1 < -5$: Add 1: $$4s < -4$$ Divide by 4: $$s < -1$$ 8. Solve inequality $2x - 3 \leq 4 + 7x$: Subtract $2x$ and 4 from both sides: $$-3 - 4 \leq 7x - 2x$$ $$-7 \leq 5x$$ Divide by 5: $$x \geq -\frac{7}{5} = -1.4$$ 9. Solve inequality $-3 \geq 8(2 - x)$: Expand right side: $$-3 \geq 16 - 8x$$ Subtract 16: $$-19 \geq -8x$$ Divide by $-8$ (flip inequality): $$\frac{19}{8} \leq x$$ 10. Solve inequality $8(x + 1) + 1 < 3(2x) + 1$: Expand: $$8x + 8 + 1 < 6x + 1$$ $$8x + 9 < 6x + 1$$ Subtract $6x + 1$: $$2x + 8 < 0$$ Subtract 8: $$2x < -8$$ Divide by 2: $$x < -4$$ 11. Solve inequality $4x - 1 \geq 4(x - 2) + 7$: Expand right side: $$4x - 1 \geq 4x - 8 + 7$$ Simplify: $$4x - 1 \geq 4x - 1$$ Subtract $4x$: $$-1 \geq -1$$ True for all $x$ (all real numbers). 12. Solve inequality $\frac{7}{4}t > -\frac{8}{3}t$: Add $\frac{8}{3}t$ to both sides: $$\frac{7}{4}t + \frac{8}{3}t > 0$$ Find common denominator 12: $$\left(\frac{21}{12} + \frac{32}{12}\right) t > 0$$ $$\frac{53}{12} t > 0$$ Since $\frac{53}{12} > 0$, multiply both sides by positive number: $$t > 0$$ 13. Solve inequality $9 - 0.1x \leq \frac{2 - 0.01x}{0.2}$: Multiply both sides by 0.2: $$0.2(9 - 0.1x) \leq 2 - 0.01x$$ $$1.8 - 0.02x \leq 2 - 0.01x$$ Subtract 1.8: $$-0.02x \leq 0.2 - 0.01x$$ Add $0.02x$: $$0 \leq 0.2 + 0.01x$$ Subtract 0.2: $$-0.2 \leq 0.01x$$ Divide by 0.01: $$-20 \leq x \Rightarrow x \geq -20$$