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Solving Equations with variables on both sides

2x – 4 = x + 5 -x -x x – 4 = 5 + 4 +4 x = 9 2(9) – 4 = 9 + 5 18 – 4 = 14 14 = 14 √. Move all variables to one side of equation subtract x from both sides Add 4 to both sides Check your answer. Solving Equations with variables on both sides. 2 – 3(x – 4) = 2(x – 5)

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Solving Equations with variables on both sides

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  1. 2x – 4 = x + 5 -x -x x – 4 = 5 + 4 +4 x = 9 2(9) – 4 = 9 + 5 18 – 4 = 14 14 = 14 √ Move all variables to one side of equation subtract x from both sides Add 4 to both sides Check your answer Solving Equations with variables on both sides

  2. 2 – 3(x – 4) = 2(x – 5) -3(x) -3(-4) 2(x) 2(-5) 2 – 3x + 12 = 2x – 10 -3x + 14 = 2x -10 +3x +3x 14 = 5x – 10 +10 + 10 24 = 5x 5 5 4 4/5 = x Distribute -3 across(watch your negative) Distribute 2 across Combine Terms on left Add 3x to both sides Add 10 to both sides Divide by 5 on both sides x = 4 4/5 X(no decimals) Solving Equations using Distributive Property

  3. 2x – 3 = 5 -4 -4(2x – 3) = (5)-4 -4 2x – 3 = -20 +3 +3 2x = -17 2 2 x = -8 ½ Multiply both sides by -4 Add 3 to both sides Divide by two on both sides x = -8 ½ (no decimals) Solving Equations with fractions

  4. ¾(2x – 4) = ¼(-x – 6) 4[¾(2x -4) = ¼(-x -6)4 3(2x – 4) = (-x – 6) 3(2x) 3(-4) = -x – 6 6x – 12 = -x – 6 +x +x 7x – 12 = -6 + 12 +12 7x = 6 7 7 x = 6/7 Multiply both sides by 4 Eliminate denominator Distribute 3 across Add x to both sides Add 12 to both sides Divide by 7 x = 6/7 More solving equations using fractions

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