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Objective - To solve equations with the variable in both sides.

Learn how to solve equations with variables on both sides. Understand the rules and techniques for isolating the variable and solving linear equations effectively. Practice various examples to enhance your skills.

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Objective - To solve equations with the variable in both sides.

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  1. Objective - To solve equations with the variable in both sides. Solve. 2x + 4 = 5x - 17 2x + 4 = 5x - 17 2x + 4 = 5x - 17 -2x -2x -5x -5x 4 = 3x - 17 -3x + 4 =-17 +17 +17 -4 -4 21 = 3x -3x = -21 3 3 -3 - 3 7 = x x = 7

  2. Rules for Solving Equations 1) Goal: Isolate the variable on one side of the equation. 2) Undo operations with their opposite operation. 3) Always do the same thing to both sides of the equation. 4) Easiest to undo add/subtract before multiply/divide.

  3. Solve. 1) 4(x - 2) - 2x = 5(x - 3) 4x - 8 - 2x = 5x - 15 2x - 8 = 5x - 15 -2x -2x -8 = 3x - 15 +15 +15 7 = 3x 3 3

  4. 2) 3(x + 2) - (2x - 4) =- (4x + 1) 3x + 6 - 2x + 4 =- 4x - 1 x + 10 =- 4x - 1 + 4x + 4x 5x + 10 = -1 - 10 -10 5x = -11 5 5 x ==

  5. 3) 5(m - 6) = 10 - 4[2(m - 7) - 5m] 5m - 30 = 10 - 4[2m - 14 - 5m] 5m - 30 = 10 - 4[-3m - 14] 5m - 30 = 10 + 12m + 56 5m - 30 = 12m + 66 -5m -5m -30 = 7m + 66 -66 -66 -96 = 7m 7 7

  6. Solve each equation below. a) 3x - 5 = 2x + 12 b) 3x + 8 = 2(x + 4) + x -2x -2x 3x + 8 = 2x + 8 + x x - 5 = 12 3x + 8 = 3x + 8 +5 +5 -3x -3x x = 17 True ! 8 = 8 One Solution Identity x = any real number c) 3x + 2 = 2(x - 1) + x 3x + 2 = 2x - 2 + x 3x + 2 = 3x - 2 -3x -3x 2 = -2 No Solution False !

  7. Solve. 4) 4(y - 2) + 6y = 7(y - 8) - 3(10 - y) 4y - 8 + 6y = 7y - 56 - 30 + 3y 10y - 8 = 10y - 86 -10y -10y -8 = -86 False Statement No Solution

  8. Solve. 5) 3(4 + k) - 2(3k + 4) = 5(k - 3) - (8k - 19) 12 + 3k - 6k - 8 = 5k - 15 - 8k + 19 -3k + 4 =-3k + 4 +3k +3k 4 = 4 True Statement Infinitely Many Solutions x = any real number

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