1. PRE-ALGEBRA

2. Lesson 7-1 Warm-Up

3. PRE-ALGEBRA 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 (7-1)

4. PRE-ALGEBRA To solve a two-step equation: 1.“undo” (work backwards) addition or subtraction (anything added or subtracted) on the variable side by doing the opposite operation to both sides of the equal sign, and 2.“undo” (work backwards) multiplication or division (anything attached to the variable) by doing the opposite operation to both sides of the equal sign. Example: Solve 3n – 6 = 10 3n – 6 = 15 Given + 6 + 6 Undo -6 from the variable side by adding 6 to both sides. 3n = 21 = Undo times 3 from the variable side by dividing both sides by 3.. 3n 3 21 3 Check: 3n – 6 = 15 3(7) – 6 8 Replace n with 7. 21 – 6 8 Multiply. 15 = 15 Simplify. Solving Two-Step Equations LESSON 7-1 Additional Examples How do you solve a two-step equation? n = 7 Simplify. 1 1 7 1 1 + 0

5. PRE-ALGEBRA Example: Lynn want to save $900 to go to Puerto Rico. She saves $45 each week and now has $180. How many more weeks will it take for Lynn to save $900. Words: $180 plus $45 each week equals $900. Define: Let w = number of additional weeks Lynn needs to save for Equation: 180 + 45 w = 900 180 + 45w = 900 Given - 180 - 180 Undo +180 from the variable side by subtracting 180 from both sides. 45w = 720 = Undo times 45 from the variable side by dividing both sides by 45.. 45n 45 720 45 Check: 180 + 45w = 900 180 + 45(16) 900 Replace w with 16. 180 + 720 900 Multiply. 900 = 900 Simplify. Solving Two-Step Equations LESSON 7-1 Additional Examples w = 16 Simplify. It will take Lynn 16 more weeks to save $900. 1 11 16 1 0 +

6. PRE-ALGEBRA Solve 5v – 12 = 8. 5v – 12 = 8 + 12 +12Add 12 to each side. 5v = 20 Simplify. v = 4Simplify. = Divide each side by 5. 5v55v5 20 5 Check: 5v – 12 = 8 5(4) – 12 8Replace v with 4. 20 – 12 8Multiply. 8 = 8Simplify. Solving Two-Step Equations LESSON 7-1 Additional Examples + 0 1 1 1

7. PRE-ALGEBRA Solve 7 – 3b = 1. 7 – 3b = 1 –7 –7 Subtract 7 from each side. -3b = -6 Simplify. b = 2Simplify. = Divide each side by –3. –3b –3 –6 –3 Solving Two-Step Equations LESSON 7-1 Additional Examples 0 + 1 1 1

8. PRE-ALGEBRA You borrow $350 to buy a bicycle. You agree to pay $100 the first week, and then $25 each week until the balance is paid off. To find how many weeks w it will take you to pay for the bicycle, solve 100 + 25w = 350. It will take you 10 weeks to pay for the bicycle. 100 + 25w = 350 – 100 – 100 Subtract 100 from each side. 25w = 250 Simplify. w = 10Simplify. = Divide each side by 25. 25w 25 250 25 Solving Two-Step Equations LESSON 7-1 Additional Examples 0 + 1 1 1

9. PRE-ALGEBRA Solve each equation. 1.12x – 14 = 102. + 7 = –4 3.9 – w = 134.–22 – = –15 5.4d – 57 = 7 r3r3 q5q5 2–33 –4 –35 16 Lesson Quiz Solving Two-Step Equations LESSON 7-1