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

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Group the terms with variables on one side of the equal sign, and simplify. Additional Example 1: Using Inverse Operations to Group Terms with Variables A. 60 – 4y = 8y 60 – 4y + 4y = 8y + 4y 60 = 12y B. –5b + 72 = –2b –5b + 72 = –2b –5b + 5b + 72 = –2b + 5b 72 = 3b Add 4y to both sides. Simplify. 60 – 4y = 8y Add 5b to both sides. Simplify. Course Solving Equations with Variables on Both Sides

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Group the terms with variables on one side of the equal sign, and simplify. A. 40 – 2y = 6y 40 – 2y + 2y = 6y + 2y 40 = 8y B. –8b + 24 = –5b –8b + 24 = –5b –8b + 8b + 24 = –5b + 8b 24 = 3b Add 2y to both sides. Simplify. 40 – 2y = 6y Add 8b to both sides. Simplify. Check It Out: Example 1 Course Solving Equations with Variables on Both Sides

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Solve. Additional Example 2A: Solving Equations with Variables on Both Sides 7c = 2c c – 2c = 2c – 2c c = c = 11 Subtract 2c from both sides. Simplify. Divide both sides by 5. Course Solving Equations with Variables on Both Sides

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Additional Example 2B: Solving Equations with Variables on Both Sides 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. Course Solving Equations with Variables on Both Sides

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Additional Example 2C: Solving Equations with Variables on Both Sides 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. Course Solving Equations with Variables on Both Sides

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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 Course Solving Equations with Variables on Both Sides

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

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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. Course Solving Equations with Variables on Both Sides

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