Question

Show two different ways to solve 2/3(3x+6)=4x+3

Answer 1

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Explanation:

Answer 2

In the two different ways we have solved the given equation as
`x=(1)/(2)`

Explanation:

Given expression is
`(2)/(3)(3x+6)=4x+3`

To simplify the given expression in two ways:

First way:

Given
`(2)/(3)(3x+6)=4x+3`

`(2)/(3)(3x+6)=4x+3`

`(6x+12)/(3)=4x+3`

Multiplying 3 on both sides

`3* ((6x+12)/(3))=3* (4x+3)`

`6x+12=12x+9`

`6x+12-12x-9=0` (adding the like terms)

`-6x+3=0`

`3(-2x+1)=0`

Dividing by 3 on both sides

`3(-2x+1)* \frac{1}3}=0* \frac{1}3}`

`(-2x+1)=0`

`-(2x-1)=0`

`2x-1=0`

`x=(1)/(2)`

Therefore the given expression is solved that
`x=(1)/(2)`

Another way:

Given
`(2)/(3)(3x+6)=4x+3`

`(2)/(3)(3x+6)=4x+3`

`2((3x)/(3)+(6)/(3))=4x+3`

`2(x+2)=4x+3`

`2x+4=4x+3`

`4x+3-2x-4=0` (adding the like terms)

`2x-1=0`

`x=(1)/(2)`

Therefore the given expression is solved that
`x=(1)/(2)`

In the two different ways we have solved the given equation as
`x=(1)/(2)`