2 6 Solving TwoStep Equations When you solve

2 -6 Solving Two-Step Equations When you solve equations that have one operation, you use an inverse operation to isolate the variable. n + 7 = 15 – 7 n = 8 You can also use inverse operations to solve equations that have more than one operation. 2 x + 3 = 23 – 3 2 x = 20 Use the inverse of mulitplication to isolate x.

2 -6 Solving Two-Step Equations Additional Example 1 A: Solving Two-Step Equations Using Division Solve. Check each answer. 9 c + 3 = 39 – 3 9 c = 36 9 9 c=4 Subtract 3 from both sides. Divide both sides by 9.

2 -6 Solving Two-Step Equations Additional Example 1 A Continued Check. 9 c + 3 = 39 ? 39 9(4) + 3 = Substitute 4 for c. ? 39 36 + 3 = ? 39 39 = 4 is a solution.

2 -6 Solving Two-Step Equations Helpful Hint Reverse the order of operations when solving equations that have more than one operation.

2 -6 Solving Two-Step Equations Additional Example 1 B: Solving Two-Step Equations Using Division Solve. Check the answer. – 34 = – 4 m – 6 +6 +6 – 28 = – 4 m – 4 7=m Add 6 to both sides. Divide both sides by – 4.

2 -6 Solving Two-Step Equations Additional Example 1 B Continued Check. – 4 m – 6 = – 34 ? – 34 – 4(7) – 6 = Substitute 7 for m. ? – 34 – 28 – 6 = ? – 34 = – 34 7 is a solution.

2 -6 Solving Two-Step Equations Check It Out: Example 1 A Solve. 3 x + 13 = 37 – 13 3 x = 24 3 3 x=8

2 -6 Solving Two-Step Equations Check It Out: Example 1 B Solve. – 33 = – 7 a – 5 +5 +5 – 28 = – 7 a – 28 = 7 a – 7 4 = a

2 -6 Solving Two-Step Equations Additional Example 2 A: Solving Two-Step Equations Using Multiplication Solve. 6 + y = 21 5 6+ – 6 (5) y 5 y 5 = 21 – 6 = 15 Subtract 6 from both sides. = (5)15 Multiply both sides by 5. y = 75

2 -6 Solving Two-Step Equations Additional Example 2 B: Solving Two-Step Equations Using Multiplication Solve. 5=z – 7 6 z 5= – 7 6 +7 +7 12 = z 6 (6)12 = z (6) 6 72 = z Add 7 to both sides. Multiply both sides by 6.

2 -6 Solving Two-Step Equations Check It Out: Example 2 A Solve. r 7 + 45 = – 60 r + 45 = – 60 7 – 45 r =– 105 7 r = (7)(– 105) (7) 7 r = – 735

2 -6 Solving Two-Step Equations Check It Out: Example 2 B Solve. p – 8 – 7 = 12 p – 7 = 12 – 8 +7 +7 p = 19 – 8 (– 8) p – 8 = (– 8)19 p = – 152

2 -6 Solving Two-Step Equations Additional 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. 00 each day. Her total cost was $127. 00. For how many days did she rent the canoe? Let d represent the number of days she rented the canoe. 7 d + 85 = 127 – 85 Subtract 85 from both sides. 7 d = 42 Divide both sides by 7. 7 d = 42 7 7 d =6 Jamie rented the canoe for 6 days.

2 -6 Solving Two-Step Equations Check It Out: Example 3 Leo and his five brothers have $40 to spend on movie tickets and popcorn. They pay $25 for the tickets. If popcorn costs $3 per box, can each person have his own box of popcorn? Explain. Let b represent the number of boxes they can afford to buy. 25 + 3 b = – 25 – 3 b = 3 b= 40 25 15 15 3 5

2 -6 Solving Two-Step Equations Check It Out: Example 3 continued No. For each person to have his own box, Leo and his brothers must buy 6 boxes (one for Leo and one for each brother). But they have enough for only 5 boxes.

2 -6 Solving Two-Step Equations Lesson Quiz Solve. Check your answers. 1. 6 x + 8 = 44 x=6 2. 14 y – 14 = 28 y = 3 m 3. 12 = 7 + 3 4. v – 8 – 6=8 63 = m v = – 112 5. Last Sunday, the Humane Society had a 3 -hour adoption clinic. During the week the clinic is open for 2 hours on days when volunteers are available. If the Humane Society was open for a total of 9 hours last week, how many weekdays was the clinic open? 3 days