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 2. 8x – 3x = 35 4k = 20 5x = 35 k = 5 x = 7 3. 3b + 2 – b = –18 4. –8 – y + 7y = 40 (3b – b) + 2 = –18 –8 + 6y = 40 2b + 2 = –18 –8 + 8 + 6y = 40 + 8 2b + 2 – 2 = –18 – 2 6y = 48 2b = –20 y = 8 b = –10 = 20 4 4k 35 5 5x 48 6 6y –20 2 2b 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 Add 2c to each side. 6c + 3 = 15 Combine like terms. 6c + 3 – 3 = 15 – 3 Subtract 3 from each side. 6c = 12 Simplify. c = 2 Simplify. Divide each side by 6. = 6c 6 12 Check 4c + 3 = 15 – 2c 4(2) + 3 15 – 2(2)   8 + 3 15 – 4 11 = 11 Substitute 2 for c. Multiply. Quick Check 7-5

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 = Jenny’s time. x Then x + 5 = Steve’s time. Equation 20 • x = 15 • (x + 5) 7-5

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. Divide each side by 5. = 5x 5 75 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 3. 2q – 4 = 5 + 5q 4. 7(v – 4) = 3(3 + v) – 1 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? 1 9 – –9 –3 9 4 deliveries 7-5