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 ID: 228589
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Slide1
Equations with the unknown on both sides.
Lesson Objective:An equation is like a set of scales.To keep it balanced, whatever youdo 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)Slide2
Solving equations:
2x + 1 = x + 5Subtract x from each sidex + 1 = 5Subtract 1 from each side x = 4Check your answer. Does the equation balance?2x4 + 1 = 4 + 5 P
Only want ‘x’ on one sideSlide3
Solving equations:
5x - 2 = 2x + 4Subtract 2x from each side3x - 2 = 4Add 2 to each side 3x = 6Divide each side by 3x = 2Check your answer. Does the equation balance?5x2 - 2 = 2x2 + 4 P
Only want ‘x’ on one sideSlide4
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 = -3Slide5
In your books: Write each equation and solve it to find x.
2x – 1 = x + 33x + 4 = x + 105x – 6 = 2x4x + 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
x = 3Slide6
Solving equations with brackets:
2 (x + 3) = x + 11Multiply out the bracket2x + 6 = x + 11Subtract x from each sidex + 6 = 11Subtract 6 from each sidex = 5Slide7
Solving equations with brackets on both sides:
2 (3x – 1 ) = 3 (x + 2)Multiply out the brackets6x - 2 = 3x + 6Subtract 3x from each side 3x -2 = + 6Add 2 to each side3x = 8Divide each side by 3x = 8/3 = 2 2/3Slide8
In your books: Write each equation and solve it to find x.
2 (x + 3) = x + 75 (2x - 1) = 3x + 92 (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)
x = 1
x = 2
x = -1
x = 5
x = -4/7
x = 15/8 = 1
7/8
x = - 7
x = -8Slide9
How could you check each answer?
2 (x + 3) = x + 75 (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 = 6 + 9
P
x = -1 means 2 (5 x-1 +2) = 5 x-1 -1
2 (-5 + 2) = -5 -1
2 x -3 = - 6
P