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**Equations with the unknown on both sides.**

Lesson Objective: An equation is like a set of scales. To keep it balanced, whatever you do to one side you must do to the other. Use this idea to solve equations like: 3x + 1 = x + 7 2 (3x + 1) = 3 (x – 2)

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**Solving equations: 2x + 1 = x + 5 Subtract x from each side x + 1 = 5**

Only want ‘x’ on one side 2x + 1 = x + 5 Subtract x from each side x + 1 = 5 Subtract 1 from each side x = 4 Check your answer. Does the equation balance? 2x = P

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**Solving equations: 5x - 2 = 2x + 4 Subtract 2x from each side**

Only want ‘x’ on one side 5x - 2 = 2x + 4 Subtract 2x from each side 3x - 2 = 4 Add 2 to each side 3x = 6 Divide each side by 3 x = 2 Check your answer. Does the equation balance? 5x = 2x P

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**On whiteboards: Solve each equation**

2x + 2 = x + 9 3x + 1 = x + 5 6x – 8 = 4x 5x + 1 = x - 11 x = 7 x = 2 x = 4 x = -3

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**In your books: Write each equation and solve it to find x.**

2x – 1 = x + 3 3x + 4 = x + 10 5x – 6 = 2x 4x + 1 = x - 8 2x + 3 = x + 10 4x – 1 = 3x + 7 Extension: 2x - 6 = - 3x + 9 x = 4 x = 3 x = 2 x = -3 x = 7 x = 8

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**Solving equations with brackets:**

2 (x + 3) = x + 11 Multiply out the bracket 2x + 6 = x + 11 Subtract x from each side x + 6 = 11 Subtract 6 from each side x = 5

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**Solving equations with brackets on both sides:**

2 (3x – 1 ) = 3 (x + 2) Multiply out the brackets 6x - 2 = 3x + 6 Subtract 3x from each side 3x -2 = + 6 Add 2 to each side 3x = 8 Divide each side by 3 x = 8/3 = 2 2/3

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**In your books: Write each equation and solve it to find x.**

2 (x + 3) = x + 7 5 (2x - 1) = 3x + 9 2 (5x + 2 ) = 5x - 1 3 (x – 1) = 2 (x + 1) 3 (3x + 2) = 2 (x + 1) 3 (4x – 3) = 2 (2x + 3) Extensions: 7(x – 2) = 3 (2x – 7) 3(3x - 1) = 5 (x – 7)

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**How could you check each answer?**

2 (x + 3) = x + 7 5 (2x - 1) = 3x + 9 2 (5x + 2 ) = 5x - 1 x = 1 means 2 (1 + 3) = 1 + 7 2 x 4 = 8 P x = 2 means 5 (2x2 -1) = 3x2 + 9 5 x 3 = P x = -1 means 2 (5 x-1 +2) = 5 x-1 -1 2 (-5 + 2) = -5 -1 2 x -3 = P

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