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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`

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