Lesson 2-1 Warm-Up

Lesson 2-1 Warm-Up

“Solving Two-Step Equations” (2-1) What is a two-step equation? How can you use a model to show how to solve a two-step equation? Two-Step Equation: an equation that involves “undoing” two operations In the following model, represents -1, represents 1, and represents a varibable, like x. This means that equals 0 (in other words, they “cancel each other out”), since 1 – 1 = 0.

“Solving Two-Step Equations” (2-1) How do you solve equations involving more than one step. To solve equations, use the addition, subtraction, multiplication, and division properties of equality which say that the equation stays equal, or balanced, if you add, subtract, multiply, or divide both sides by the same number. Simply use the properties of equality repeatedly to get the variable alone on one side of the equation with a coefficient of 1 (Examples: 1x, 1t, 1c)

= + 5 Subtract 5 from each side. - 5 - 5 Solving Two-Step Equations LESSON 2-1 Additional Examples Solve 13 = + 5. y 3 = + 5 Subtract 5 from each side. - 5 - 5 y 3 8 = Simplify. y 3 3 • 8 = 3 • Multiply each side by 3. y 3 24 = y Simplify. y 3 Check: 13 = + 5 24 3 13 + 5 Substitute 24 for y. 13 8 + 5 13 = 13

cost times number of plus shipping equals amount Solving Two-Step Equations LESSON 2-1 Additional Examples You order iris bulbs from a catalog. Iris bulbs cost $0.90 each. The shipping charge is $2.50. If you have $18.50 to spend, how many iris bulbs can you order? Words: cost times number of plus shipping equals amount per iris iris bulbs to spend bulb Define: Let b = the number of bulbs you can order. Equation: 0.90 • b + 2.50 = 18.50 0.90b + 2.50 = 18.50 0.90b + 2.50 – 2.50 = 18.50 – 2.50 Subtract 2.50 from each side. 0.90b = 16 Simplify.

= Divide each side by 0.90. b = 17.7 Simplify. You can order 17 bulbs. Solving Two-Step Equations LESSON 2-1 Additional Examples (continued) 0.90b 0.90 = 16 0.90 Divide each side by 0.90. b = 17.7 Simplify. You can order 17 bulbs. Check:  Is the solution reasonable? You can only order whole iris bulbs. Since 18 bulbs would cost 18 • 0.90 = 16.20 plus $2.50 for shipping, which is more than $18.50, you can only order 17 bulbs.

–y + 7 = –12 Subtraction Property of Equality - 7 - 7 Solving Two-Step Equations LESSON 2-1 Additional Examples Solve –y + 7 = –12. –y + 7 = –12 Subtraction Property of Equality - 7 - 7 –y = –19 Simplify. (–1)(–y) = (–1)(–19) Multiplication Property of Equality y = 19 Simplify. Check: –y + 7 = –12 –(19) + 7 –12 Substitute 19 for y. –12 = –12

Solve 8 = + 4. Justify each step. Solving Two-Step Equations LESSON 2-1 Additional Examples Solve 8 = + 4. Justify each step. c 24 8 = + 4 Subtraction Property of Equality -4 - 4 c 24 4 = Simplify. c 24 24(4) = 24 Multiplication Property of Equality (Multiply both sides by 24.) c 24 96 = c Simplify.

5. What is the justification for the following step? 12 – 2y = 46 Solving Two-Step Equations LESSON 2-1 Lesson Quiz Solve each equation. 1. 3b + 8 = –10 2. –12 = –3x – 9 3. – + 7 = 14 4. –x – 13 = 35 5. What is the justification for the following step? 12 – 2y = 46 12 – 2y – 12 = 46 – 12 –6 1 c 4 –28 –48 Subtr. Prop. of Equality