1. **Simplify the expression** $3 + 2(5x - 6)$. Step 1: Apply the distributive property: $2 \times 5x = 10x$ and $2 \times (-6) = -12$. Step 2: Rewrite the expression: $3 + 10x - 12$. Step 3: Combine like terms: $3 - 12 = -9$. Final simplified expression: $$10x - 9$$. 2. **Simplify each expression:** (a) $\frac{7}{x} - \frac{3}{x} + \frac{1}{x}$ Step 1: Since all terms have the same denominator $x$, combine the numerators: $$\frac{7 - 3 + 1}{x} = \frac{5}{x}$$ (b) $\frac{y}{x} + \frac{m}{2x}$ Step 1: Find a common denominator, which is $2x$. Step 2: Rewrite the first fraction: $\frac{y}{x} = \frac{2y}{2x}$. Step 3: Add the fractions: $$\frac{2y}{2x} + \frac{m}{2x} = \frac{2y + m}{2x}$$ 3. **Solve for $x$ in the equation:** $$9^x \times 9^2 = 9^{12}$$ Step 1: Use the property of exponents: $a^m \times a^n = a^{m+n}$. Step 2: Combine the left side: $$9^{x+2} = 9^{12}$$ Step 3: Since the bases are equal, set the exponents equal: $$x + 2 = 12$$ Step 4: Solve for $x$: $$x = 12 - 2 = 10$$ **Final answers:** 1. $10x - 9$ 2. (a) $\frac{5}{x}$, (b) $\frac{2y + m}{2x}$ 3. $x = 10$