# algebra & linear sum..

```Academic Skills Advice
Summary
Algebra
Writing Algebraic Expressions:
Write a sentence in maths instead of English by assigning letters to numbers.
Example:

Half of a number plus quarter of another number: can be written
𝒙
𝟐
+
𝒚
𝟒
Simplifying Expressions:
An algebraic expression can be simplified by collecting all the ‘like terms’ together.
Example:

Simplify the following:
𝟑𝒂 (𝒃 – 𝒄) + 𝟓𝒂𝒃 (First remove the bracket then simplify).
After multiplying out the brackets we have: 3𝑎𝑏 − 3𝑎𝑐 + 5𝑎𝑏 = 𝟖𝒂𝒃 − 𝟑𝒂𝒄
Solving Equations with one Unknown:
When solving this type of 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: 6(2Q + 13) = -9(Q + 3)
(collect Q’s at one side, numbers at the other.)
Starting Equation.
Multiply out the brackets
Take 78 from each side
Tidy up.
Divide each side by 21 to leave ‘Q’ on its own.
6(2Q + 13)
12Q + 78
12Q + 78 - 78
12Q + 9Q
21Q
Q
=
=
=
=
=
=
-9(Q + 3)
-9Q - 27
-9Q - 27 - 78
-105 – 9Q + 9Q
-105
-5
A quick method:
When something crosses to the other side of the equals sign it does the opposite.
E.g. + becomes -, x becomes &divide; and vice versa.
Example:

Solve the equation: 𝟏𝟐𝒌 + 𝟒 − 𝟑𝒌 + 𝟏𝟎 = 𝟒𝟏
Starting Equation.
Collect 𝑘’s at one side, numbers at the other.
Tidy up
X9 crosses the “=” sign and becomes &divide;9.
&copy; H Jackson 2011 / ACADEMIC SKILLS
Notice that +4 swapped sides and
became -4, and +10 swapped sides
and became -10.
12𝑘 + 4 − 3𝑘 + 10 =
12𝑘 − 3𝑘 =
9𝑘 =
𝒌 =
41
41 − 4 − 10
27
𝟑
1
```