12-3 Solving Equations with Variables on Both Sides Warm Up Solve. 1. 6n + 8 – 4n = –4w + 16 – 4w = – t – 17 – 13t = = 2(x + 7) + 4 n = 6 w = 6 t = 7 x = –3

12-3 Solving Equations with Variables on Both Sides Problem of the Day You buy 1 cookie on the first day, 2 on the second day, 3 on the third day, and so on for 10 days. Your friend pays $10 for a cookie discount card and then buys 10 cookies at half price. You both pay the same total amount. What is the cost of one cookie? $0.20

12-3 Solving Equations with Variables on Both Sides Learn to solve equations that have variables on both sides.

12-3 Solving Equations with Variables on Both Sides Group the terms with variables on one side of the equal sign, and simplify. Example 1: A. 60 – 4y = 8y 60 – 4y + 4y = 8y + 4y 60 = 12y Add 4y to both sides. (If you subtracted 8y From both sides, you Would have 0 left on The right and you do Not want that.) Simplify. 60 – 4y = 8y 12 5 = y

12-3 Solving Equations with Variables on Both Sides Solve. Example 2 7c = 2c c – 2c = 2c – 2c c = c = 11 Subtract 2c from both sides. Simplify. Divide both sides by 5.

12-3 Solving Equations with Variables on Both Sides Additional Example 2B Solve. 49 – 3m = 4m – 3m + 3m = 4m + 3m = 7m – 14 = 7m + 14 – = 7m = m Add 3m to both sides. Simplify. Subtract 14 from both sides. Divide both sides by 7.

12-3 Solving Equations with Variables on Both Sides Additional Example 2C 2525 x = 1515 x– x =x = 1515 x 2525 x –x = 1515 x 1515 x – 1515 x = 1515 x(5)(–12) ‏ = (5) ‏ x = –60 Subtract 1515 x from both sides. Simplify. Multiply both sides by 5.

12-3 Solving Equations with Variables on Both Sides Solve. 8f = 3f f – 3f = 3f – 3f f = f = 13 Subtract 3f from both sides. Simplify. Divide both sides by 5. Check It Out: Example 2A

12-3 Solving Equations with Variables on Both Sides Solve. 54 – 3q = 6q – 3q + 3q = 6q + 3q = 9q – 9 = 9q + 9 – 9 45 = 9q 5 = q Add 3q to both sides. Simplify. Subtract 9 from both sides. Divide both sides by 9. Check It Out: Example 2B 45 = 9 9 9q9q

12-3 Solving Equations with Variables on Both Sides 2323 w = 1313 w– 9– w =w = 1313 w– w –w = 1313 w 1313 w – 1313 w = 1313 w(3)(–9) ‏ = (3) ‏ w = –27 Subtract 1313 w from both sides. Simplify. Multiply both sides by 3. Check It Out: Example 2C Solve.

12-3 Solving Equations with Variables on Both Sides Christine can buy a new snowboard for $ She will still need to rent boots for $8.50 a day. She can rent a snowboard and boots for $18.25 a day. How many days would Christine need to rent both the snowboard and the boots to pay as much as she would if she buys the snowboard and rents only the boots for the season? Additional Example 3: Consumer Math Application

12-3 Solving Equations with Variables on Both Sides Additional Example 3 Continued 18.25d = d 18.25d – 8.5d = d – 8.5d 9.75d = d = 14 Let d represent the number of days. Subtract 8.5d from both sides. Simplify. Divide both sides by Christine would need to rent both the snowboard and the boots for 14 days to pay as much as she would have if she had bought the snowboard and rented only the boots.

12-3 Solving Equations with Variables on Both Sides 1.Group the terms with variables on one side of the equal sign, and simplify. 19p = 10p A. 9p = –54 B. 29p = –54 C. 29p = 54 D. 9p = 54 Lesson Quiz for Student Response Systems

12-3 Solving Equations with Variables on Both Sides 2. Solve m = –7m – 26 A. m = –9 B. m = –7 C. m = 9 D. m = 7 Lesson Quiz for Student Response Systems

12-3 Solving Equations with Variables on Both Sides 3.Matthew orders T-shirts from an online store for $25 each and an additional $20 for shipping. Mike buys the same kind of T-shirts at a local shop for $27 each. If Matthew and Mike spent the same amount, how many T-shirts did each of them buy? A. 5 T-shirts B. 10 T-shirts C. 15 T-shirts D. 20 T-shirts Lesson Quiz for Student Response Systems