SIMPLE LINEAR EQUATIONS

CONTENT

1. Definition of Equation
2. Solving Simple Equations (balance methods; collecting like terms).
3. Solving Equations Involving Brackets and Fractions
4. Word Problems Leading to Simple Equations

Definition of Equation

Equations are open sentences that have the equality sign (=). Solving an equation means finding a value of the unknown which makes the equation true. Any letter a, f, c, x, etc. can be used as unknown. The set of values which make an equation true is called the truth set.

Solving Simple Equations

Example 1:

Solve the following simple equations:

(i) 3a − 8 = 10

(ii) 10x − 7 = 27

(iii) 4 + 5y = 19

Solution:

(i) 3a – 8 = 10

Method 1

3a – 8 + 8 = 10 + 8

3a = 18

\(\frac{3a}{3} = \frac{18}{3} = 6\)

Method 2

3a – 8 = 10

3a = 10 + 8

3a = 18

\(a = \frac{18}{3} = 6\)

Note: If a number is moved from one side to an equation over the equal sign to the other side, the sign of the number changes.