2Warm Up Solve. 1. n + 9 = 17 2. 6x = 42 3. 71 – z = 55 n = 8 4. x = 7 y8= 9y = 72
3CaliforniaStandardsPreview of Grade AF4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
4When you solve equations that have one operation, you use an inverse operation to isolate the variable.n + 7 = 15– –7n = 8You can also use inverseoperations to solve equations that have more than one operation.2x + 3 = 23– 3 – 32x = 20Use the inverse of multiplying by 2 to isolate x.x = 10
5Reverse the order of operations when solving equations that have more than one operation. Helpful Hint
6Additional Example 1A: Solving Two-Step Equations Using Division Solve. Check your answer.9c + 3 = 399c + 3 = 39– 3 –3Subtract 3 from both sides.9c = 369c9= 36Divide both sides by 9.c = 4
7Additional Example 1A Continued Check.9c + 3 = 399(4) + 3?=39Substitute 4 for c.?=?=4 is a solution.
8Additional Example 2: Solving Two-Step Equations Using Multiplication Solve.y5A. 6 += 21y56 += 21– –6Subtract 6 from both sides.y5= 15(5)y5= (5)15Multiply both sides by 5.y = 75
9Additional Example 3: Consumer Math Application Jamie rented a canoe while she was on vacation. She paid a flat rental fee of $85.00, plus $7.50 each day. Her total cost was $ For how many days did she rent the canoe?Let d represent the number of days she rented the canoe.7.5d + 85 = 130– –85Subtract 85 from both sides.7.5d = 457.5d = 45Divide both sides by 22.214.171.124.5d = 6Jamie rented the canoe for 6 days.
10Check It Out! Example 1BSolve. Check the answer.–6m – 8 = –50–6m – 8 = –50Add 8 to both sides.–6m = –42–6m–6= –42Divide both sides by –6.m = 7
11Subtract 8 from both sides. = 40 Check It Out! Example 2Solve.y2A. 8 += 48y28 += 48– –8Subtract 8 from both sides.y2= 40y2= (2)40Multiply both sides by 2.(2)y = 80
12Subtract 25 from both sides. Check It Out! Example 3Jack’s father rented a car while they were on vacation. He paid a rental fee of $20.00 per day, plus 20¢ a mile. He paid $25.00 for mileage and his total bill for renting the car was $ For how many days did he rent the car?Let d represent the number of days he rented the car.20d + 25 = 165– – 25Subtract 25 from both sides.20d = 14020d = 140Divide both sides by 20.2020d = 7Jack’s father rented the car for 7 days.
13Solve. Check your answers. 1. 6x + 8 = 44 2. 14y – 14 = 28 3. 4. x = 6 Lesson QuizSolve. Check your answers.1. 6x + 8 = 442. 14y – 14 = 283.4.x = 6y = 3m712 =63 = mv–8– 6 = 8v = –1125. Last Sunday, the Humane Society had a 3-houradoption clinic. During the week the clinic is openfor 2 hours on days when volunteers are available.If the Humane Society was open for a total of 9hours last week, how many weekdays was theclinic open?3 days