1. 2-8 Solving Two-Step Equations Warm Up Solve. 1. x + 12 = 35 2. 8x = 120 3. = 7 4. –34 = y + 56 x = 23 x = 15 y = 63 y = –90 y9y9 Lesson 23

2. 2-8 Solving Two-Step Equations Learn to solve two-step equations. Lesson 23

3. 2-8 Solving Two-Step Equations Sometimes more than one inverse operation is needed to solve an equation. Before solving, ask yourself, “ What is being done to the variable, and in what order? ” Then work backward to undo the operations. Lesson 23

4. 2-8 Solving Two-Step Equations The mechanic ’ s bill to repair your car was $850. The mechanic charges $35 an hour for labor, and the parts that were used cost $275. How many hours did the mechanic work on your car? Lesson 23

5. 2-8 Solving Two-Step Equations 1 Understand the Problem The answer is the number of hours the mechanic worked on your car. List the important information: Let h represent the hours the mechanic worked. The parts cost $275. The labor cost $35 per hour. The total bill was $850. Total bill=Parts+Labor 850=275+35h Lesson 23

6. 2-8 Solving Two-Step Equations Think: First the variable is multiplied by 35, and then 275 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 275 from both sides of the equation, and then divide both sides of the new equation by 35. 2 Make a Plan Lesson 23

7. 2-8 Solving Two-Step Equations 850 = 275 + 35h Solve 3 –275 –275 Step 1: Subtract to undo the addition. 575= 35h 16.4  h The mechanic worked for about 16.4 hours on your car. Step 2: Divide to undo multiplication. 575 35h 35 = Lesson 23

8. 2-8 Solving Two-Step Equations Look Back4 You can use a table to decide whether your answer is reasonable. $870$27559517 $835$27556016 $800$27552515 $765$27549014 $730$27545513 Total CostPartsLaborHours 16.4 hours is a reasonable answer. Lesson 23

9. 2-8 Solving Two-Step Equations Solve + 7 = 22. Think: First the variable is divided by 3, and then 7 is added. To isolate the variable, subtract 7, and then multiply by 3. Subtract 7 from both sides. n3n3 + 7 – 7 = 22 – 7 n3n3 Multiply both sides by 3. 3  = 3  15 n3n3 n = 45 Work backward to isolate the variable. Lesson 23

10. 2-8 Solving Two-Step Equations Solve = 9. y – 4 3 Work backward to isolate the variable. Think: First the variable is being subtracted by 4 and then is divided by 3. To isolate the variable, multiply by 3 and then add 4. (3) Add 4 to both sides. Multiply both sides by 3. Y – 4 = 27 +4 +4 y = 31 Lesson 23 y – 4 3 = 9

11. 2-8 Solving Two-Step Equations Solve + 8 = 18. Think: First the variable is divided by 4, and then 8 is added. To isolate the variable, subtract 8, and then multiply by 4. Subtract 8 from both sides. n4n4 + 8 – 8 = 18 – 8 n4n4 Multiply both sides by 4. 4  = 4  10 n4n4 n = 40 Work backward to isolate the variable. Lesson 23

12. 2-8 Solving Two-Step Equations Solve = 7.y – 7 2 = 7 y – 7 2 y – 7 = 14 + 7 + 7Add to undo subtraction. y = 21 Multiply both sides by the denominator. Multiply both sides of the equation by the denominator. = 7 y – 7 2 (2) (2) ‏ Lesson 23

13. 2-8 Solving Two-Step Equations Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems Lesson 23

14. 2-8 Solving Two-Step Equations Solve. 1. – 3 = 10 1.3. –8.3 = –3.5x + 13.4 3. The cost for a new cell phone plan is $39 per month plus a one-time start-up fee of $78. If you are charged $1014, how many months will the contract last? x = –117 x = 6.2 24 x –9 Lesson 23

15. 2-8 Solving Two-Step Equations Solve. 1. – 3 = 10 2. 7y + 25 = –24 3. –8.3 = –3.5x + 13.4 4. = 3 5. The cost for a new cell phone plan is $39 per month plus a one-time start-up fee of $78. If you are charged $1014, how many months will the contract last? Lesson Quiz y = –7 x = –117 x = 6.2 y = 28 24 x –9 y + 5 11

16. 2-8 Solving Two-Step Equations 1. Solve – 9 = 3. A. p = –84 B. p = –42 C. p = 42 D. p = 84 Lesson Quiz for Student Response Systems p -7

17. 2-8 Solving Two-Step Equations 2. Solve 3r + 46 = –29. A. r = –20 B. r = –25 C. r = –30 D. r = –35 Lesson Quiz for Student Response Systems

18. 2-8 Solving Two-Step Equations 3. Solve –3.3 = –1.2t + 15.3. A. t = 15.5 B. t = 14 C. t = 12.5 D. t = 10 Lesson Quiz for Student Response Systems

19. 2-8 Solving Two-Step Equations 4. Solve = 5. A. v = 31 B. v = 32 C. v = 33 D. v = 34 Lesson Quiz for Student Response Systems v + 7 8

20. 2-8 Solving Two-Step Equations 5. The membership fee of a DVD rental store is $15. The cost of renting a DVD is $2. If John pays $27, how many DVDs did he rent? A. 6 DVDs B. 8 DVDs C. 12 DVDs D. 24 DVDs Lesson Quiz for Student Response Systems