Lesson 1.2 Essential Question: How do I solve an equation with more than one step? Objective: To use two or more transformations (steps) to solve an equation Keys to successfully solving multi-step equations. 1. Simplify one or both sides of the equation when possible. a. Combine like terms b. Use distributive property. 2. Use inverse operations to isolate the variable. a. Add, Subtract, Multiply or Divide b. Multiply by a reciprocal. Vocabulary: Reciprocal If is a nonzero number, then its reciprocal is

Example: 8x – 3x + 4 = 14 Combine like terms 8x – 3x 5x + 4 = 14 Subtract 4 from each side – 4 – 4 5x = 10 Divide each side by 5 Simplify each side x = 2 Check: Insert 2 for x in the original equation 8(2) – 3(2) + 4 = 14 16 – 6 + 4 = 14 14 = 14 checks

Example: 17 = 2(3x + 1) – x Distribute the 2. 2(3x +1) 17 = 6x + 2 – x Combine like terms 6x – x 17 = 5x + 2 Subtract 2 from each side – 2 – 2 15 = 5x Divide both sides by 5 Simplify 3 = x Check: Replace the x with 3 17 = 2(3·3 + 1) – 3 17 = 2(10) – 3 17 = 20 – 3 Checks

Example: Multiplying by the reciprocal Subtract 13 from each side –13 – 13 Multiply each side by the reciprocal of which is Simplify x = – 12

Write a summary of today’s notes Write a summary of today’s notes. Write a left column question about when to use the reciprocal to solve an equation.