1. **Problem:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula:** To isolate $x$, use the subtraction property of equality: if $a + b = c$, then $a = c - b$. 3. **Work:** $$x + 2 = 4$$ Subtract 2 from both sides: $$x + \cancel{2} - \cancel{2} = 4 - 2$$ $$x = 2$$ 4. **Explanation:** We subtract 2 from both sides to keep the equation balanced and isolate $x$. The value of $x$ is 2. --- 1. **Problem:** Find the common denominator for fractions $\frac{1}{3}$ and $\frac{1}{4}$. 2. **Formula:** The common denominator is the least common multiple (LCM) of the denominators. 3. **Work:** Denominators are 3 and 4. Multiples of 3: 3, 6, 9, 12, 15... Multiples of 4: 4, 8, 12, 16... The smallest common multiple is 12. 4. **Explanation:** The least common denominator is 12, which allows us to rewrite both fractions with the same denominator. --- 1. **Problem:** Find the hypotenuse length of a right triangle with legs 3 and 4 feet. 2. **Formula:** Use the Pythagorean theorem: $$c = \sqrt{a^2 + b^2}$$ where $c$ is the hypotenuse. 3. **Work:** $$c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$ 4. **Explanation:** The hypotenuse is 5 feet long, calculated by taking the square root of the sum of the squares of the legs.