Linear Equations

Linear Equations

A Linear Equation is an equation whose graph is a straight line. Each term has a degree of at most 1. Each term can have degree 0 (constant term) or degree 1. A linear equation in one variable is an equation that involves only one variable x. Geeral form of linear equation can be written as ax + b = 0. There are no higher or lower order terms such as x2, x3 or x1/2.

Example 1: 6x + 5 = 0 is a linear equation. Note that it is in the form ax + b = 0, where a and b are constants. In this case a = 6 and b = 2. Any equation which can be reduced to form ax + b is also called linear equation.

Example 2: 7x + 3 = 9, this can be written as 7x - 6 = 0

Example 3: 2(x + 1) = 6(x - 4) is also a linear equation.

Solving Linear Equations

Any linear equation can have only one solution. If you solve a linear equation, you will get one value of x. Solving linear equations is very simple. First, open all brackets and take all terms involving x to Left Hand Side (LHS) and constant terms to Right Hand Side (RHS). Then, using simple additions and subtractions, you will get the value of x.

Example 4:

2(x + 1) = 6(x - 4)
2x + 2 = 6x - 24
2x - 6x = - 24 - 2
- 4x = - 26
4x = 26
x = 26/4
x = 13/2 or 6.5