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:

- Three times a certain number plus 20 is equal to the number plus 12.
- A woman is p years old. In seven years’time, she will be 45 years old.
- 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:

- 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**:

- A certain number is added to 15, the result is six minus the same number.
- 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**

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

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