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Transcript
Lesson 2-1 Warm-Up ALGEBRA 1 Lesson 2-1 Warm-Up ALGEBRA 1 “Solving Two-Step Equations” (2-1) What is a two-step equation? Two-Step Equation: an equation that involves “undoing” two operations How can you use a model to show how to solve a two-step equation? 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. ALGEBRA 1 “Solving Two-Step Equations” (2-1) How do you solve To solve equations, use the addition, subtraction, multiplication, and equations involving more division properties of equality which say that the equation stays equal, than one step. 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) ALGEBRA 1 Solving Two-Step Equations LESSON 2-1 Additional Examples Solve 13 = 13 = y +5 3 -5 8= -5 y 3 Check: 13 = 13 13 Subtract 5 from each side. Simplify. 3•8= 3• y 24 = y y + 5. 3 3 y +5 3 24 +5 3 Multiply each side by 3. Simplify. Substitute 24 for y. 8+5 13 = 13 ALGEBRA 1 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 0.90b = 16 Subtract 2.50 from each side. Simplify. ALGEBRA 1 Solving Two-Step Equations LESSON 2-1 Additional Examples (continued) 0.90b 16 = 0.90 0.90 b = 17.7 Divide each side by 0.90. 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. ALGEBRA 1 Solving Two-Step Equations LESSON 2-1 Additional Examples Solve –y + 7 = –12. –y + 7 -7 –y = –12 - 7 = –19 (–1)(–y) = (–1)(–19) y = 19 Subtraction Property of Equality Simplify. Multiplication Property of Equality Simplify. Check: –y + 7 = –12 –(19) + 7 –12 Substitute 19 for y. –12 = –12 ALGEBRA 1 Solving Two-Step Equations LESSON 2-1 Additional Examples Solve 8 = c + 4. Justify each step. 24 c 8 = 24 + 4 -4 -4 c 4 = 24 24(4) = Subtraction Property of Equality Simplify. c 24 24 Multiplication Property of Equality (Multiply both sides by 24.) 96 = c Simplify. ALGEBRA 1 Solving Two-Step Equations LESSON 2-1 Lesson Quiz Solve each equation. 1. 3b + 8 = –10 –6 2. –12 = –3x – 9 1 3. – c + 7 = 14 4 –28 4. –x – 13 = 35 –48 5. What is the justification for the following step? 12 – 2y = 46 12 – 2y – 12 = 46 – 12 Subtr. Prop. of Equality ALGEBRA 1