**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;

y^{2} – 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.”

**Your turn: **

Solve the following by calculating a value for x:

**5x-25=75**