Transcript Starter: back of books

Lesson Objective:
Solving equations with
the unknown on both sides.
Year 8:
Level 6
Equations like:
• 3x + 1 = x + 7
• 2 (3x + 1) = 3 (x – 2)
Lesson Outcomes:
At end of Lesson each one of you must be
able to solve these type of equations.
Starter
Multiplying out one bracket
(Expanding brackets)
How do you multiply out 2(x +7) ?
X
x
7
2
2x
14
= 2x + 14
2 (x +7)
= 2x + 14
In Your Books
Solve for x:
8 x  7  121
Answer
57
1
x   or  14
4
4
Remember
An equation is like a set of scales.
To keep it balanced, whatever you
do to one side you must do to the
other.
Operations
Inverse Operations
+
-
-
+




Solving equations:
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?
2x4 + 1 = 4 + 5 P
Solving equations:
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?
5x2 - 2 = 2x2 + 4 P
On whiteboards: Solve each equation
A) 2x + 2 = x + 9
x=7
B) 3x + 1 = x + 5
x=2
C) 6x – 8 = 4x
x=4
D) 5x + 1 = x - 11
x = -3
In your books:
Write each equation and solve it to find x.
A) 2x – 1 = x + 3
x=4
B) 3x + 4 = x + 10
x=3
C) 5x – 6 = 2x
x=2
D) 4x + 1 = x - 8
x = -3
E) 2x + 3 = x + 10
x=7
F) 4x – 1 = 3x + 7
x=8
Extension:
2x - 6 = - 3x + 9
x=3
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
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
In your books:
Write each equation and solve it to find x.
A) 2 (x + 3) = x + 7
x=1
B) 5 (2x - 1) = 3x + 9
x=2
C) 2 (5x + 2 ) = 5x - 1
x = -1
D) 3 (x – 1) = 2 (x + 1)
x=5
E) 3 (3x + 2) = 2 (x + 1)
x = -4/7
F) 3 (4x – 3) = 2 (2x + 3)
x = 15/8 = 1 7/8
Extensions: 7(x – 2) = 3 (2x – 7)
3(3x - 1) = 5 (x – 7)
x=-7
x = -8
Plenary
A) 2 x + 6 = x + 7
B) 5 (2x - 1) = 3x + 9
C) 2 (5x + 2 ) = 5x - 1
A) 2 x + 6 = x + 7
Plenary
x = 1 means 2 (1 + 3) = 1 + 7
2x4=8 P
B) 5 (2x - 1) = 3x + 9
x = 2 means 5 (2x2 -1) = 3x2 + 9
5x3=6+9P
C) 2 (5x + 2 ) = 5x - 1
x = -1 means 2 (5 x-1 +2) = 5 x-1 -1
2 (-5 + 2) = -5 -1
2 x -3 = - 6 P