You can add or subtract like with like.
When asked to simplify you bring the same things together.
Example:
Answer:
Simplify x 2 - 4x - 3.
2x 2 - 6x + 4 - x 2 + 2x - 7
Brackets mean multiply. Always simplify your answer if you can.
Example: Remove the brackets and simplify 3 ( 2 x – 7 ) – 5 ( x – 4 )
Answer: 6 x – 21 - 5 x + 2 0
X – 1
Watch the ” back to back” brackets!
Example: Remove the brackets and simplify
Answer: 2 x ( 3 x – 4 ) - 3 ( 3 x – 4 )
6 x 2 – 8 x – 9 x + 1 2
6 x 2 – 1 7 x + 1 2
( 2 x – 3 ) ( 3 x – 4 )
x = 2 and y = - 3
Example: Find the value of 3 x 2 – 4 x y – 2 y 2
3 ( 2 ) 2 – 4 ( 2 ) ( - 3 ) – 2 ( - 3 ) 2
3 ( 4 ) – 8 ( - 3 ) - 2 ( 9 )
1 2 + 2 4 - 1 8 = 3 0
MAKE SURE YOU CAN USE THE FRACTION BUTTON ON YOUR CALCULATOR.
Mrs Mc Guinness Page 1

EQUATIONS:
When you have an equal sign in a question we then call it an equation.
With an equal sign

You can do what you like to it but make sure you do it to both sides.

You can bring numbers over the equal sign but make sure you do the opposite on the other side. Example: +5 becomes -5 x3 becomes ÷3 x-4 becomes ÷-4
Example: Solve 3 ( 2x – 6 ) = 2 ( 2 x + 1 )
6 x – 1 8 = 4 x + 2
6 x – 4 x = 2 + 18
2 x = 2 0 x = 1 0
NOTE: When you are asked to ” solve” your answer is always “ x = “
When you are asked to solve try to get the x on its own on the left hand side.
FRACTIONS WITH AN EQUAL SIGN :
When you have an equal sign with fractions , multiply across the top with all of the denominators to eliminate the fraction and then get x on its own.
Example: Solve
Mrs Mc Guinness
2 ( 3 x – 1 ) – 3 ( x - 3 ) = 4 ( 4 )
6 x – 2 – 3 x + 9 = 1 6
6 x – 3 x = 1 6 + 2 – 9
3 x = 9
X = 3
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DIVISION

The order in which you do the operations are divide, multiply, subtract and add.

Only divide the first number with the first number and put your answer on top.

Multiply this answer with the outside number and put it on the bottom.

Change all the signs on the bottom line and add

Then you start all over again.
X 2 - 4
Example: 2x+3
ANSWER : X 2 - 4
2x 3 + 3x 2
-8x - 12
-8x - 12
0
FRACTIONS with no equal sign:
Always get a common denominator . Divide with the bottom line and multiply your answer with the top line.
Example one: =
(divide 3 into 12 to get 4 and multiply your answer with 2 to get 8 and then divide 4 into 12 to get 3 and multiply your answer by 3 to get 9)
Example two:
Mrs Mc Guinness Page 3

Example three:
R = real numbers (every number)
N = Natural numbers (every positive whole number)
Z = Integers (every whole number both positive and negative)
Example: Show on a numberline 3x - 7 ≤ 5
3X ≤ 12
X
X ≤ 4
-1_________0_________1________2_________3_________4_________5
Example two: -5 ≤ 3 X + 1 < 7
Separate both inequalities and solve both separately and then combine them on the numberline.
-5 ≤ 3x+1
-3x ≤ 1 + 5
3x+1 < 7 x < 2
-3x ≤ 6
3x ≥ -2
Mrs Mc Guinness Page 4