Transcript Equations & Brackets

Equations & Brackets.
You are now going to solve more complex equations by
combining together two ideas that you have seen already .
Try the following questions to make sure you are ready:
Idea 1:
Idea 2 :
Solve the equation
Multiply out the bracket
3x – 6 = 18
3 ( 2x – 4 )
Solution :
Solution :
x=8
6x – 12
We are now going to combine these two ideas together to
solve the equations on the following pages.
Solving Equations.
Example 1 .
Solve the equation :
2 ( x + 4 ) = 14
Solution.
2( x + 4 ) = 14
Multiply out the bracket first.
2x + 8 = 14
Subtract 8 from both sides.
2x = 6
Divide both sides by 2 .
x=3
Hint: check the solution by substituting
x = 3 into the original equation.
Example 2 .
Solve
Solve the equation :
2 ( 3x + 2 ) = 28
Solution:
2( 3x + 2 ) = 28
6x + 4 = 28
What should you do first ?
Multiply out the bracket.
What comes next ?
6x = 24
Subtract 4 from each side.
x=4
What comes next ?
Check your answer by
putting x = 4 back into
the bracket.
Divide each side by 6.
Example 3 .
Solve the equation :
5( x – 3 ) = 20
Solution.
5 ( x – 3 ) = 20
What does 5 times –3 equal.
5x – 15 = 20
-15
5x = 35
What must you do to both sides?
x=7
Add 15
Check the answer.
What Goes In The Box 1 ?
Solve the following equations:
(1) 2 ( x + 4 ) = 14
x=3
(2) 3 ( 2x + 5 ) = 27
x=2
(3) 5 ( 2x + 6 ) = 100
x=7
(4) 4 ( 3x – 5 ) = 40
x=5
(5) 7 ( 2 x – 6 ) = 28
x=5
(6) 3 ( 4 + 2x ) = 30
x=3