Area Houghton Mifflin Harcourt Publishing Company Equations with 11.2 Rational Numbers ? LESSON ESSENTIAL QUESTION Solving an Equation that Involves Fractions To solve an equation with the variable on both sides that involves fractions, start by eliminating the fractions from the equation. EXAMPLE 1 Solven+2=3n+2. 10 STEP 1 STEP 2 STEP 3 Determine the least common multiple of the denominators: LCM(10, 5, 2) = 10 Multiply both sides of the equation by the LCM. 10 (n+3)=10 (3n+2) How can you solve equations with rational number coefficients and constants? 5 10 (n) + 10 (2)=10 (3n) + 10(2) 7n+15= 6n +20 Use inverse operations to solve the equation. 6n + 20 - 15 7n+15 - 15 7n -6n n = 6n + 5 -6n 5 TEKS 8.8.C 10 10 x 1 = 5 x 2 = 2x5 Subtract 15 from both sides. TEKS Expressions, equations, and relationships-8.8.A Write one-variable equations ... with variables on both sides... using rational number coefficients and constants. Also 8.8.B, 8.8.C Subtract 6n from both sides. Reflect 1. What is the advantage of multiplying both sides of the equation by the least common multiple of the denominators in the first step? Math On the Spot my.hrw.com The constant on the right side, 2, is not a fraction. Why do you still need to multiply it by the LCM, 10? 2. What If? What happens in the first step if you multiply both sides by a common multiple of the denominators that is not the LCM? Math Talk Mathematical Processes Lesson 11.2 303​