Solving Linear Equations
Revision Notes
Simple Equations

You need to do the same to both sides

You need to do the opposite operation (e.g. add becomes subtract, multiply
becomes divide)

Remember negative rules

+ x + = +
+ ÷ + = +
- x - = +
- ÷ - = +
- x + = -
- ÷ + = -
+ x - = -
+ ÷ - = -
If the answer is not a whole number, leave it as a fraction
Examples
1.
Solve 3x + 2 = 17 (-2 off both sides)
3x = 15 (÷3)
x=5
2.
Solve 7y – 3 = 34 (+ 3)
7y = 37 (÷7)
y=
37
7
=5
𝟐
𝟕
3. Solve 10 – 2a = 25 (-10)
-2a = 15 (÷ -2)
a=-
15
2
= -7
𝑓
4. Solve 2 + = - 10 (-2)
6
𝑓
6
= -12 ( x 6)
f = - 72
*remember it is –2a
𝟏
𝟐
Equations with brackets


Always expand the bracket first (this is worth 1 mark)
Then solve like a simple equation
Examples
1.
Solve 3(2x + 1) = 24
(expand the bracket)
6x + 3 = 24
( - 3)
6x = 21 (÷ 6)
x=
2.
21
6
=3
Solve 40 = 4(5y – 2)
𝟏
𝟐
(expand the bracket)
40 = 20y – 8
( + 8)
48 = 20y
(÷ 20)
48
20
=y
y=2
8
20
=2
𝟐
𝟓
Equations with letters on both sides


Avoid negative letters where possible
Group the letters on one side and numbers on the other
Examples
1.
Solve 3x + 1 = x + 9
2x + 1 = 9
2x = 8
( - x)
(- 1)
(÷ 2)
x=4
2.
Solve 5y – 3 = 2 (4y + 3) (expand the bracket)
5y – 3 = 8y + 6
(-5y)
-3 = 3y + 6
( - 6)
-9 = 3y (÷ 3)
y = -3
Key Points





Do the same to both sides
You need to do the opposite operation (add becomes subtract, multiply becomes divide)
Multiply any brackets out first (this is worth one mark)
Group letters on one side and numbers on the other
Leave answers as fractions – there is no need to convert to decimals
Practice
1.
5x + 3 = 33
x = ____________________
2.
2 (7y – 1) = 26
y = _____________________
3.
6x + 3 = 2x + 11
x = ______________________
4.
3 (y + 2) = 10 – 2y
y = ________________________
5.
𝑎
4
+3= 9
a = _________________________
6.
3𝑚+1
5
= 6
m = _______________________
Exam Questions
Q1.
Q2.
Q3.
Q4.
Mock Exam Questions