Linear equations in one variable

Linear Equations in One Variable

6.1

Linear Equations in One Variable

Definition

A linear equation that has only one variable and the power of the variable is \(1\).

General form: \(ax+b=c\)

Symbol	Usage
\(=\)	To show the relationship between two quantities that have the same value
\(\neq\)	To show the relationship that consists of different values

Example

Subtract \(8\) from a number and its remainder is \( 2\).

The equation is \(x-8=2\).

We can see that it is a linear equation because the equation has one variable, \(x\) and the power of \(x\) is \(1\).

Solve linear equations in one variable:

Solution of linear equation is also known as the root of the equation.
Has only one solution.
In a linear equation, the value on the left hand side is always equal to the value on the right hand side.

Example

Calculate:

(i) \(3(x+2)=5x\)

(ii) \(\dfrac{x}{6}+3=5\)

(i)

\(\begin{aligned}3(x+2)&=5x \\\\3x+6&=5x \\\\3x+6-6&=5x-6 \\\\3x&=5x-6 \\\\3x-5x&=5x-6-5x \\\\-2x&=-6 \\\\\dfrac{-2x}{-2}&=\dfrac{-6}{-2} \\\\x&=3. \end{aligned}\)

(ii)

\(\begin{aligned}\dfrac{x}{6}+3&=5 \\\\\bigg(\dfrac{x}{6}\times6\bigg)+(3\times6)&=5\times6 \\\\x+18&=30 \\\\x+18-18&=30-18 \\\\x&=12. \end{aligned}\)