Equations with the unknown on both sides Lesson

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: • 3 x + 1 = x + 7 • 2 (3 x + 1) = 3 (x – 2)

Solving equations: Only want ‘x’ on one side 2 x + 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? 2 x 4 + 1 = 4 + 5 P

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

On whiteboards: Solve each equation A) 2 x + 2 = x + 9 x=7 B) 3 x + 1 = x + 5 x=2 C) 6 x – 8 = 4 x x=4 D) 5 x + 1 = x - 11 x = -3

In your books: Write each equation and solve it to find x. A) 2 x – 1 = x + 3 x=4 B) 3 x + 4 = x + 10 x=3 C) 5 x – 6 = 2 x x=2 D) 4 x + 1 = x - 8 x = -3 E) 2 x + 3 = x + 10 x=7 F) 4 x – 1 = 3 x + 7 x=8 Extension: 2 x - 6 = - 3 x + 9 x=3

Solving equations with brackets: 2 (x + 3) = x + 11 Multiply out the bracket 2 x + 6 = x + 11 Subtract x from each side x + 6 = 11 Subtract 6 from each side x=5

Solving equations with brackets on both sides: 2 (3 x – 1 ) = 3 (x + 2) Multiply out the brackets 6 x - 2 = 3 x + 6 Subtract 3 x from each side 3 x -2 = + 6 Add 2 to each side 3 x = 8 Divide each side by 3 x = 8/3 = 2 2/3

In your books: Write each equation and solve it to find x. 2 (x + 3) = x + 7 x=1 B) 5 (2 x - 1) = 3 x + 9 x=2 C) 2 (5 x + 2 ) = 5 x - 1 x = -1 D) 3 (x – 1) = 2 (x + 1) x=5 E) 3 (3 x + 2) = 2 (x + 1) x = -4/7 F) 3 (4 x – 3) = 2 (2 x + 3) x = 15/8 = 1 7/8 Extensions: 7(x – 2) = 3 (2 x – 7) 3(3 x - 1) = 5 (x – 7) x=-7 x = -8 A)

How could you check each answer? A) 2 (x + 3) = x + 7 x = 1 means 2 (1 + 3) = 1 + 7 2 x 4=8 P B) 5 (2 x - 1) = 3 x + 9 x = 2 means 5 (2 x 2 -1) = 3 x 2 + 9 5 x 3=6+9 P C) 2 (5 x + 2 ) = 5 x - 1 x = -1 means 2 (5 x-1 +2) = 5 x-1 -1 2 (-5 + 2) = -5 -1 2 x -3 = - 6 P