Solving Equations with Variables on Both Sides

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Presentation transcript:

Solving Equations with Variables on Both Sides

Example Solve. Check. 10a 10a = 7a + 21 10a = 7a+ 21 7a – 7a – 7a 10(7) = 7(7)+ 21 3 3a = 21 70 = 49 + 21 3 3 70 = 70  7 a =

Example Solve. Check. 5x 5x = 9x 9x + 32 5x = 9x + 32 – 9x – 9x 5(-8) = 9(-8)+ 32 -4x -4 = 32 -40 = -72 + 32 -4 -4 -40 =- 40  x = -8

Example (Same problem) Solve. Check. 5x 5x = 9x 9x + 32 5x = 9x + 32 – 5x – 5x 5(-8) = 9(-8)+ 32 = 4x + 32 - 32 - 32 -40 = -72 + 32 = 4x - 32 -40 = -40  4 4 -8 = x

Example Solve. Check. 12x 12x = 7x 7x + 45 12x = 7x + 45 – 7x - 7x 12(9) = 7(9)+ 45 5x 5 = 45 108 = 63 + 45 5 5 108 = 108  x = 9

Example Solve. Check. 5x 3x - 1 5x + 1 = 3x - 1 5x + 1 = 3x -3x -3x 4(-1)+1 = 3(-1)- 1 2x + 1 + 1 = -1 -1 -5 + 1 = -3 - 1 - 1 -1 2x = -2 -4 = -4  2 2 x = -1

Example Solve. Check. -x -x + 3 -3x + 9 -x + 3 = -3x + 9 = -3x +3x +3x -(3)+3 = -3(3) + 9 2x + 3 + 3 = +9 +9 0 = -9 + 9 - 3 - 3 2x = 6 0 = 0  2 2 x = 3

Example 8x + 2 (3x + 5) = 7x + 10 8x + 8x 6x 6x + 10 = 7x + 10 7x 7x - 10 - 10 7x = 7 7 x = 0

Check 8x + 2 (3x + 5) = 7x + 10 8(0) + 2[3(0) + 5] = 7(0) + 10 0 + 2[ 0 + 5] = 0 + 10 0 + 2[ 5] = 10 0 + 10 = 10 10 = 10 