Solved Examples: Representing the solution of a linear equation on a number line

Solved Example 1

`2x + 3 = 6`

Solution

Solve the equation. Subtract 3 from both sides of the equation,

`2x + 3 - 3 = 6 - 3`
`2x = 3`

Divide throughout by 2,

`(2x)/2 = 3/2`
`x = 3/2`

Mark `x = 3/2 = 1.5` on a number line,

Solution of `2x + 3 = 6`

Solved Example 2

`4x + 1 = 5x + 2`

Solution

Solve the equation. Subtract 1 from both sides of the equation,

`4x + 1 - 1 = 5x + 2 - 1`

Simplify,

`4x = 5x + 1`

Subtract 5x from both sides of the equation,

`4x - 5x = 5x + 1 - 5x`
`-x =1`

Multiply throughout by -1,

`-1 * -x = -1 * 1`
`x = -1`

Mark x = -1 on a number line,

Solution of 4x + 1 = 5x + 2

Solved Example 3

`x/2 = x/3 + 3`

Solution

First, solve the equation. Subtract `x/3` from both sides of the equation,

`x/2 - x/3 = x/3 + 3 - x/3`

Simplify,

`x/6 = 3`

Multiply throughout by 6,

`x/6 * 6 = 3 * 6`
`x = 18`

Now mark 18 on a number line.

Solution of `x/2 = x/3 + 3`

Solved Example 4

`3x + 2 = 4x - 15`

Solution

Solve the equation. Subtract 2 from both sides of the equation,

`3x + 2 - 2 = 4x - 15 - 2`

Simplify,

`3x = 4x - 17`

Subtract 4x from both sides of the equation,

`3x - 4x = 4x - 17 - 4x`

Simplify,

`-x = -17`

Multiply throughout by -1,

`-x * -1 = -17 * -1`
`x = 17`

Mark x = 17 on a number line.

Solution of 3x + 2 = 4x - 15

Solved Example 5

`x + 2 = 3`

Solution

Solve the equation. Subtract 2 from both sides of the equation,

`x + 2 - 2 = 3 - 2`

Simplify,

`x = 1`

Graph x = 1 on a number line.

Solution of x + 2 = 3