Question

How do you solve `4[2( - 5x + y ) - y]= 10( y - 4x )`?

Answer 1

`y = 0`

Explanation:

`4 [ 2( -5x +y) - y ] = 10 (y - 4x)`

Step 1: Open the brackets. First the innermost on left-hand-side and the one on right- hand- side

`4 [ - 10x + 2y - y ] = 10y - 40x`

Step 2: Simplify

`4 [ -10x + y] = 10y -40x`

Step 3: Open the square bracket:

`-40x + 4y = 10y - 40x`

Step 4: Bring the terms with variable `x` on left- hand side of the equation and take the terms with `y` variable on right-hand-side. Or vice versa.

Transposition

`- 40x + 40x = 10y - 4y`

Step 5: Solve
`0x = 6y`
or
`6y = 0x`
i.e.
`y = 0`

Cross check by substituting the obtained value of `y` in the given equation:

`4 [ 2( -5x +y) - y ] = 10 (y - 4x)`

`4 [ 2 (-5x + 0)- 0 ] = 10 (0 - 4x)`

`4 [ -10x] = 10 (-4x)`

`- 40 x = - 40x`

Left-hand-side = right-hand-side