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Solving Equations With Variables on Both Sides PRE-ALGEBRA LESSON 7-5 (For help, go to Lesson 7-2.) Solve each equation. 1. k + 3k = 20 2. 8x – 3x = 35 3. 3b + 2 – b = –18 4. –8 – y + 7y = 40 Check Skills You’ll Need 7-5 Solving Equations With Variables on Both Sides PRE-ALGEBRA LESSON 7-5 Solutions 1. k + 3k = 20 4k = 20 2. 8x – 3x = 35 5x = 35 4k 20 = 4 4 5x 35 = 5 5 k=5 x=7 3. 3b + 2 – b (3b – b) + 2 2b + 2 2b + 2 – 2 2b = –18 = –18 = –18 = –18 – 2 = –20 4. –8 – y + 7y –8 + 6y –8 + 8 + 6y 6y = 40 = 40 = 40 + 8 = 48 6y 48 = 6 6 2b –20 = 2 2 y =8 b = –10 7-5 Solving Equations With Variables on Both Sides PRE-ALGEBRA LESSON 7-5 Solve 4c + 3 = 15 – 2c. 4c + 3 = 15 – 2c 4c + 2c + 3 = 15 – 2c + 2c 6c + 3 = 15 6c + 3 – 3 = 15 – 3 Combine like terms. Subtract 3 from each side. 6c = 12 Simplify. 6c 12 = 6 6 Divide each side by 6. c=2 Check Add 2c to each side. Simplify. 4c + 3 = 15 – 2c 4(2) + 3 15 – 2(2) Substitute 2 for c. 8 + 3 15 – 4 Multiply. 11 = 11 7-5 Quick Check Solving Equations With Variables on Both Sides PRE-ALGEBRA LESSON 7-5 Steve types at a rate of 15 words/min and Jenny types at a rate of 20 words/min. Steve and Jenny are both typing the same document, and Steve starts 5 min before Jenny. How long will it take Jenny to catch up with Steve? words Jenny types = words Steve types Words 20 words/min • Jenny’s time = 15 words/min • Steve’s time Let x = Jenny’s time. Then Equation 20 = Steve’s time. x+5 • = x 7-5 15 • (x + 5) Solving Equations With Variables on Both Sides PRE-ALGEBRA LESSON 7-5 (continued) 20x = 15(x + 5) 20x = 15x + 75 Use the Distributive Property. 20x – 15x = 15x – 15x + 75 Subtract 15x from each side. 5x = 75 Combine like terms. 5x 75 = 5 5 Divide each side by 5. x = 15 Simplify. Jenny will catch up with Steve in 15 min. 7-5 Solving Equations With Variables on Both Sides PRE-ALGEBRA LESSON 7-5 (continued) Check Test the result. At 20 words/min for 15 min, Jenny types 300 words. Steve’s time is five min longer. He types for 20 min. At 15 words/min for 20 min, Steve types 300 words. Since Jenny and Steve each type 300 words, the answer checks. Quick Check 7-5 Solving Equations With Variables on Both Sides PRE-ALGEBRA LESSON 7-5 Solve each equation. 1. 3 – 2t = 7t + 4 – 2. 18 + 6z = 4z 1 9 3. 2q – 4 = 5 + 5q –9 4. 7(v – 4) = 3(3 + v) – 1 –3 9 5. You work for a delivery service. With Plan A, you can earn $5 per hour plus $.75 per delivery. With Plan B, you can earn $7 per hour plus $.25 per delivery. How many deliveries must you make per hour to earn the same amount from either plan? 4 deliveries 7-5