Question

How do you solve `-[ x - ( - 7x + 4) ] = 6- ( - 4x + 7)`?

Answer 1

`x=5/12`

Explanation:

First, expand the equation,
`-[x+7x-4]=6+4x-7`
`-x-7x+4=4x-1`

Group similar terms on one side:
x to a side, numbers to a side
`4x+7x+x=4+1`

`12x=5`
`x=5/12`

Answer 2

`x=5/12`

Explanation:

`"distribute the 'inner' bracket on the left side"`

`-[x+7x-4]=6-(-4x+7)`

`-8x+4=6+4x-7larr" distribute throughout"`

`-8x+4=4x-1larr" simplify right side"`

`"subtract 4x from both sides"`

`-8x-4x+4=cancel(4x)cancel(-4x)-1`

`rArr-12x+4=-1`

`"subtract 4 from both sides"`

`-12xcancel(+4)cancel(-4)=-1-4`

`rArr-12x=-5`

`"divide both sides by - 12"`

`(cancel(-12) x)/cancel(-12)=(-5)/(-12)`

`rArrx=5/12`

`color(blue)"As a check"`

Substitute this value into the equation and if the left side equals the right side then it is the solution.

`-((8xx5/12)-4)=-(40/12-48/12)=8/12=2/3`

`6-((-4xx5/12)+7)=72/12-64/12=8/12=2/3`

`rArrx=5/12" is the solution"`