Solved Examples - Mult-step linear equations

Solved Example 1

`2x + 1 = 3`

Solution

Write the original equation,

`2x + 1 = 3`

Subtract 1 from both sides of the equation,

`2x + 1 - 1 = 3 - 1`

Simplify,

`2x = 2`

Divide throughout by 2,

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

Simplify,

`x = 1`

Solved Example 2

`4x - 2 = 4`

Solution

Write the original equation

`4x - 2 = 4`

Add 2 to both sides of the equation,

`4x- 2 + 2 = 4 + 2`

Simplify,

`4x= 6`

Divide throughout by 4,

`(4x)/4 = 6/4`

`x = 3/2`

Solved Example 3

`2x = 3 - x`

Solution

Write the original equation,

`2x = 3 - x`

Add x to both sides,

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

Simplify,

`3x = 3`

Divide throughout by 3,

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

Simplify,

`x = 1`

Solved Example 4

`3x + 4 = 5x - 3`

Solution

Write the original equation,

`3x + 4 = 5x - 3`

Subtract 4 from both sides of the equation,

`3x + 4 - 4 = 5x - 3 - 4`

Simplify,

`3x = 5x - 7`

Subtract `5x` from both sides of the equation,

`3x - 5x = 5x - 7 - 5x`

Simplify,

`-2x = -7`

Divide throughout by -2,

`(-2x)/(-2) = (-7)/(-2)`

`x = 7/2`

Solved Example 5

`x/2 + 1 = x/3 + 2`

Solution

Subtract 1 from both sides of the equation,

`x/2 + 1 - 1 = x/3 + 2 - 1`

Simplify,

`x/2 = x/3 + 1`

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

`x/2- x/3 = x/3 + 1 - x/3`

Simplify,

`x/6 = 1`

Multiply throughout by 6,

`x/6 * 6 = 1 * 6`

`x = 6`