# Algebra Revision Foundation

## 06 – More on Equations

What is a Linear Equation:

An equation is a statement involving an unknown number, typically called x.

In a “linear” equation, x is only to the first power. e.g. 6x = 9; 2x + y = 7;

y2 – 4 = 5 is not a linear equation because it has a squared term.

Solving Linear equations:

A linear equation can be written as a function, with f(x) instead of y,

so f(x) = 3x – 1 rather than y = 3x – 1

Solving any equation corresponds to the four operations of arithmetic.

1. If x + a = b, then x = b – a.

“If a number is added on one side of an equation, we may subtract it on the other side.”

2. If x – a = b, then x = b + a.

“If a number is subtracted on one side of an equation, we may add it on the other side.”

3. If ax = b, then x = b ÷ a

“If a number multiplies one side of an equation, we may divide it on the other side.”

4. If x÷a = b, then x = ab.

“If a number divides one side of an equation, we may multiply it on the other side.”