1. Solve $x - 9 = 12$ for $x$. Start by isolating $x$ on one side. Add 9 to both sides: $$x - 9 + 9 = 12 + 9$$ Simplify: $$x = 21$$ 2. Solve $x + 5 = 11$ for $x$. Subtract 5 from both sides: $$x + 5 - 5 = 11 - 5$$ Simplify: $$x = 6$$ 3. Solve $4x = 28$ for $x$. Divide both sides by 4: $$\frac{\cancel{4}x}{\cancel{4}} = \frac{28}{4}$$ Simplify: $$x = 7$$ 4. Solve $3x + 6 = 18$ for $x$. Subtract 6 from both sides: $$3x + 6 - 6 = 18 - 6$$ Simplify: $$3x = 12$$ Divide both sides by 3: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{12}{3}$$ Simplify: $$x = 4$$ 5. Solve $\frac{5}{2} - 2 = 3$ for $x$. This equation has no $x$, so no solution for $x$ is needed. Possibly a typo. 6. Solve $3(x - 2) = 2(x + 4)$ for $x$. Distribute both sides: $$3x - 6 = 2x + 8$$ Subtract $2x$ from both sides: $$3x - 2x - 6 = 2x - 2x + 8$$ Simplify: $$x - 6 = 8$$ Add 6 to both sides: $$x - 6 + 6 = 8 + 6$$ Simplify: $$x = 14$$ 7. Solve $10 = \frac{2x}{4} - 3$ for $x$. Add 3 to both sides: $$10 + 3 = \frac{2x}{4} - 3 + 3$$ Simplify: $$13 = \frac{2x}{4}$$ Rewrite $\frac{2x}{4}$ as $\frac{2}{4}x = \frac{1}{2}x$: $$13 = \frac{1}{2}x$$ Multiply both sides by 2: $$2 \times 13 = 2 \times \frac{1}{2}x$$ Simplify: $$26 = x$$ 8. Solve $\frac{x + 3}{2} = \frac{2x - 5}{3}$ for $x$. Cross multiply: $$3(x + 3) = 2(2x - 5)$$ Distribute: $$3x + 9 = 4x - 10$$ Subtract $3x$ from both sides: $$3x - 3x + 9 = 4x - 3x - 10$$ Simplify: $$9 = x - 10$$ Add 10 to both sides: $$9 + 10 = x - 10 + 10$$ Simplify: $$19 = x$$ 9. Solve $|x + 2| = 6$ for $x$. Recall $|A| = B$ means $A = B$ or $A = -B$. So: $x + 2 = 6$ or $x + 2 = -6$ Solve each: $x + 2 = 6$: Subtract 2: $$x = 4$$ $x + 2 = -6$: Subtract 2: $$x = -8$$ 10. Solve $|2x - 5| = 9$ for $x$. Set up two equations: $2x - 5 = 9$ or $2x - 5 = -9$ Solve each: $2x - 5 = 9$: Add 5: $$2x = 14$$ Divide by 2: $$x = 7$$ $2x - 5 = -9$: Add 5: $$2x = -4$$ Divide by 2: $$x = -2$$