Question

Solve each for X. Show your work

1). 1/2x - 1/4 = 3/5x + 2


2). 10-1/2x = 6 + 3x

Answer 1

1).
`x = (8)/(7)`

2).
`x = - (45)/(2)`

Explanation:

1)
`10 - (1)/(2) x = 6 + 3x`

`20 - x = 12 + 6x`

`20 - x - 6x = 12 + 6x - 6x`

`20 - x - 6x = 12`

`- x - 6x = 12 - 20`

`- 7x = 12 - 20`

`- 7x = - 8`

`x = (8)/(7)`

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2)
`x = - (45)/(2)`

`(1)/(2) x - (1)/(4) = (3)/(5) x + 2`

`20( (1)/(2) x - (1)/(4) ) = 20( (3)/(5) x + 2)`

`20 * (1)/(2) x - 20 * (1)/(4) = 20( (3)/(5) x + 2)`

`10x - 20 * (1)/(4) = 20 * (3)/(5) x + 20 * 2`

`10x - 5 = 20 * (3)/(5) x + 20 * 2`

`10x - 5 = 4 * 3x + 20 * 2`

`10x - 5 = 4 * 3x + 40`

`10x - 5 - 12x = 40`

`10x - 12x = 40 + 5`

`- 2x = 40 - 5`

`- 2x = 45`

`x = - (45)/(2)`