Question

What is 1/4 (x-3)=3x-11/4x-3

Answer 1

No solution for
`(1)/(4)(x-3)=3x-(11)/(4)x-3`

Explanation:

We can solve the equation by isolating x through order of operations. We use PEMDAS in reverse by undoing SADMEP or subtraction, addition, division, multiplication, exponents, and parenthesis.

1. We simplify any parenthesis. We multiply by 1/4 on the left side.

`(1)/(4) (x-3)=3x-(11)/(4)x-3\\(1)/(4)x-(1)/(4)(3)=3x-(11)/(4)x-3`

`(1)/(4)x-(3)/(4) =3x-(11)/(4)x-3`

2. We undo any subtraction or addition by doing the inverse on both sides.

`(1)/(4) x-(3)/(4) +(3)/(4)=3x-(11)/(4)x-3+(3)/(4)\\(1)/(4) x=3x-(11)/(4)x-(9)/(4)`

3. Add like terms for x on the right side then subtract from both sides.

`(1)/(4) x=(1)/(4)x-(9)/(4)\\(1)/(4) x-(1)/(4)x=(1)/(4)x-(1)/(4)x-(9)/(4)\\0x=0x-(9)/(4)\\0\\eq- (9)/(4)`

Our answer is no solution because no variable remains and the equation is false.