Solving One-Step Equations Lesson 4 Linear Equations Solving One-Step Equations

Warm-Up Evaluate each expression for x = −4. x + 7 3x − 1 −x x2

Solving One-Step Equations Target: Use inverse operations to solve one-step equations.

The Properties of Equality For any numbers a, b and c: If a = b then a + c = b + c (Addition Property of Equality) If a = b then a – c = b – c (Subtraction Property of Equality) If a = b then a ∙ c = b ∙ c (Multiplication Property of Equality) If a = b then a ÷ c = b ÷ c (Division Property of Equality)

Vocabulary Zero Pair: One positive integer chip paired with one negative integer chip. Inverse Operation: Operations that undo each other.

Example 1ab Solve for x. Check your solution. x – 6 = 22 + 6 + 6 + 6 + 6 x = 28 28 – 6 = 22 8x = 88 8 8 x = 11 8(11) = 88

Example 1cd Solve for x. Check your solution. x + 10 = – 7 – 10 – 10 – 10 – 10 x = – 17 (– 17) + 10 = – 7

Example 2a Write an equation for the statement. Solve the equation and check your solution. The product of eleven and a number is seventy-seven. 11x = 77 11 11 x = 7 11(7) = 77

Example 2b Write an equation for the statement. Solve the equation and check your solution. The sum of a number and 52 is 98. x + 52 = 98 – 52 – 52 x = 46 46 + 52 = 98

Example 2c Write an equation for the statement. Solve the equation and check your solution. A number decreased by 13 is 214. x – 13 = 214 + 13 + 13 x = 227 227 – 13 = 214

Example 3 The sum of Kirk’s age and his dad’s age is 53. Kirk is 14. Write an equation that represents this situation using d to represent the dad’s age. Solve the equation and check your solution. 14 + d = 53 – 14 – 14 d = 39 14 + 39 = 53 Kirk’s dad is 39 years old.

Exit Problems Solve each equation for x. x – 70 = 138 11x = 66

Communication Prompt How are manipulatives helpful when solving one-step equations?