HW # 25- p. 100 # all BRING AN EGG CARTON Warm up Week 7, Day One Solve. a)Y = -49d) - h = b) 4.7m = c) k-3.2 = -6.8

Warm Up Response Solve. a)Y = d) - h = b) 4.7m = c) k-3.2 =

2-8 Two-Step Equations with Rational Numbers

Recall that two-step equations contain two operations, and therefore, require two inverse operations to solve. Before solving, ask yourself, “ What is being done to the variable, and in what order? ” One method to solve the equation is to work backward to undo the operations.

The mechanic ’ s bill to repair Mr. Wong ’ s car was $ The mechanic charges $45.50 an hour for labor, and the parts that were used cost $ How many hours did the mechanic work on the car? Problem Solving Application

Continued 1 Understand the Problem The answer is the number of hours the mechanic worked on the car. List the important information: Let h represent the hours the mechanic worked. The parts cost $ The labor cost $45.50 per hour. The total bill was $ Total bill=Parts +Labor = h

Think: First the variable is multiplied by 45.50, and then is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract from both sides of the equation, and then divide both sides of the new equation by Make a Plan Continued

= h Solve 3 – = 45.50h 4.6 = h The mechanic worked for 4.6 hours on Mr. Wong ’ s car. Continued Since h is multiplied by 45.50, divide both sides by h = Since is added to both sides, subtract from both sides.

You can use a table to decide whether your answer is reasonable. Look Back4 Continued HoursLaborPartsTotal Cost 1$45.50$443.75$ $91.00$443.75$ $136.50$443.75$ $182.00$443.75$ $227.50$443.75$ hours is a reasonable answer.

Example 2 n + 7 = 22 3 n + 7 = n = * n = 15 * 3 3 n = 45

Example 3 Solve = 9. y – 4 3 = 9 y – 4 3 y – 4 = Since 4 is subtracted from y, add 4 to both sides to undo the subtraction. y = 31 Multiply both sides by the denominator. Method 2: Multiply both sides of the equation by the denominator. = 9 y – 4 3 (3)

Example 4 Solve + 8 = 18. N4N4 + 8 – 8 = 18 – 8 n4n4 Since n is divided by 4, multiply both sides by 4. 4  = 4  10 N4N4 n = 40 Method 1: Use fraction operations. + 8 = 18 N4N4 Since 8 is added to, subtract 8 from both sides to undo the addition. n4 = 10 N4N4

Solve. 1. – x – 3 = y = – –8.3 = –3.5x = 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 $ , how many months will the contract last? Lesson Quiz y = –7.4 x = –117 x = 6.2 y = months 1919 y

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? EXTRA EXAMPLES: Example 1

Check It Out! Example 1 Continued 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

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 Make a Plan Check It Out! Example 1 Continued

850 = h Solve 3 – = 35h 16.4  h The mechanic worked for about 16.4 hours on your car. Check It Out! Example 1 Continued h 35 = Since h is multiplied by 35, divide both sides by 35. Since 275 is added to both sides, subtract 275 from both sides.

Look Back4 Check It Out! Example 1 Continued You can use a table to decide whether your answer is reasonable. HoursLaborPartsTotal Cost 13$455$275$730 14$490$275$765 15$525$275$800 16$560$275$835 17$595$275$ hours is a reasonable answer.