Academic Skills Advice
Linear Equations Summary
Solving Linear Equations:
When solving a linear equation you are trying to find the value of the letter in the equation.
To do this you need to make the letter the subject of the equation.
Example:

Solve the equation: 6(2𝑄 + 13) = −9(𝑄 + 3)
(Do this by collecting 𝑄’s at one side and numbers at the other.)
Starting Equation:
Multiply out the brackets:
Take 78 from each side:
Tidy up:
Add 9Q to each side:
Tidy up:
6(2𝑄 + 13)
12𝑄 + 78
12𝑄 + 78 − 78
12𝑄
12𝑄 + 9𝑄
21𝑄
=
=
=
=
=
=
−9(𝑄 + 3)
−9𝑄 − 27
−9𝑄 − 27 − 78
−9𝑄 − 105
−9𝑄 − 105 + 9𝑄
−105
Divide each side by 21 to leave ‘Q’
on its own:
21𝑄
21
=
−105
21
Simplify and tidy up:
𝑄
=
−5
A quick method:
When something crosses to the other side of the equals sign it does the opposite.
E.g. + becomes -, x becomes ÷ and vice versa.
Example:

Solve the equation: 5(3𝑘 + 4) − 3(4𝑘 − 5) = 41
Starting Equation:
Multiply out the brackets
Collect like terms (k’s and numbers):
+35 crosses the “=” sign and becomes -35:
Tidy up:
3 crosses the “=” sign and divides
Tidy up:
© H Jackson 2011/2014 / Academic Skills
5(3𝑘 + 4) − 3(4𝑘 − 5)
15𝑘 + 20– 12𝑘 + 15
3𝑘 + 35
3𝑘
3𝑘
𝑘
=
=
=
=
=
=
𝑘 =
41
41
41
41 − 35
6
6
3
2
1