1. The problem: Solve $2x+3=7$ for $x$. 2. Subtract $3$ from both sides: $2x=7-3$ 3. Simplify: $2x=4$ 4. Divide both sides by $2$: $x=\frac{4}{2}$ 5. Simplify: $x=2$ 1. The problem: Factor $x^2-9$ 2. Recognize a difference of squares: $x^2-9=(x)^2-(3)^2$ 3. Factor as $(x-3)(x+3)$ 1. The problem: Solve $x^2-5x+6=0$ 2. Factor the quadratic: $(x-2)(x-3)=0$ 3. Use zero product property: $x-2=0$ or $x-3=0$ 4. Solve: $x=2$ or $x=3$ 1. The problem: Simplify $(3x^2)(2x^3)$ 2. Multiply coefficients: $3 \times 2=6$ 3. Apply exponent rule: $x^{2+3}=x^5$ 4. Result: $6x^5$ 1. The problem: Solve for $y$ in $3y-4=11$ 2. Add $4$ to both sides: $3y=11+4$ 3. Simplify: $3y=15$ 4. Divide both sides by $3$: $y=5$ 1. The problem: Find slope of line passing through points $(1,2)$ and $(3,8)$ 2. Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ 3. Substitute points: $m=\frac{8-2}{3-1}=\frac{6}{2}$ 4. Simplify: $m=3$ 1. The problem: Simplify expression $(x^3y^2)^2$ 2. Apply power to each factor: $x^{3\times2}y^{2\times2}$ 3. Result: $x^6y^4$ 1. The problem: Solve for $x$: $4x-7=9$ 2. Add $7$ to both sides: $4x=16$ 3. Divide both sides by $4$: $x=4$ 1. The problem: Calculate $5!$ 2. Factorial definition: $5!=5\times4\times3\times2\times1$ 3. Multiply: $5\times4=20$, $20\times3=60$, $60\times2=120$, $120\times1=120$ 4. Result: $120$ 1. The problem: Simplify $(2x+3)^2$ 2. Use square of a binomial: $(a+b)^2=a^2+2ab+b^2$ 3. Substitute $a=2x$, $b=3$: $(2x)^2 + 2(2x)(3) + 3^2$ 4. Calculate: $4x^2 + 12x + 9$