Simple Equations

An algebraic equation is two algebraic expressions separated by an equal sign. The left hand side is equal to the right hand side (LHS = RHS)

e.g     7 + 3 = 10,  20 -6 = 14,  4 x 5 = 20, 35/7 = 5

Translation of algebraic equations into words: Any letter of the alphabet can be used to represent the unknown number.

Translation of algebraic sentences into equations:

Example: Translate the following into equations:

1. Three times a certain number plus 20 is equal to the number plus 12.
2. A woman is p years old. In seven years’time, she will be 45 years old.
3. The result of taking 10 from the product of a certain number and 7 is the same as taking 4 from twice the number.

Solution:

1. Let the number be m

3 x m + 20 = m + 12

i.e 3m + 20 = m + 12

• Woman is p years old;

7 years’ time, she will be (p + 7) years

i.e p + 7 = 45

• Let the number be a,

Product of a and 7 = 7a

Taking 10 from 7a = 7a – 10

Taking 4 from twice the number = 2a – 4

Then, 7a – 10 = 2a – 4

Evaluation:Translate to algebraic equations:

1. A certain number is added to 15, the result is six minus the same number.
2. Ayo is y years old, 7 years ago, she was 15 years old.

Solving Linear Simple Equations Involving Collection of Like Terms

Simple equations can be solved by collecting like terms. That is taking the unknown like terms to one side and the known to the other side.

Example:

Solve the following equations:

• 2y + 3 = y + 1           (b) 4c – 8 = 10 – 5c

Solution

• 2y + 3 = y + 1

Subtract y from both sides to eliminate y from RHS

2y – y + 3 = y – y + 1

y + 3 = 1

Subtract 3 from both sides to eliminate 3 from LHS

y + 3 – 3 = 1 – 3

y = -2

• 4c – 8 = 10 – 5c

Collect like terms by adding 5c to both sides to eliminate 5c from the RHS

4c + 5c – 8 = 10 – 5c + 5c

9c – 8 = 10

Add 8 to both sides to eliminate 8 from LHS

9c – 8 + 8 = 10 + 8

9c = 18

Divide both sides by 9

C = 2

Theory

1. Solve the linear equations (a) x – 2 = 2x + 1    (b) 19x – 12 = 11x + 4
2. Subtracting nine from a certain number gives thirteen.