Question

How do you solve `(3x-1)/(5x+4 )= 4`?

Answer 1

`x=-1`

Explanation:

`"to eliminate the fraction multiply both sides by "5x+4`

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

`rArr3x-1=4(5x+4)larrcolor(blue)"distribute"`

`rArr3x-1=20x+16`

`"subtract "20x" from both sides"`

`3x-20x-1=cancel(20x)cancel(-20x)+16`

`rArr-17x-1=16`

`"add 1 to both sides"`

`-17xcancel(-1)cancel(+1)=16+1`

`rArr-17x=17`

`"divide both sides by "-17`

`(cancel(-17) x)/cancel(-17)=(-17)/17`

`rArrx=-1`

`color(blue)"As a check"`

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

`(-3-1)/(-5+4)=(-4)/(-1)=4=" right side"`

`rArrx=-1" is the solution"`

Answer 2

`(5x+4)*(3x-1)/(5x+4)=4*(5x+4)`
therefore `3x-1= 20x+16`
`-16-1=20x-3x`
`-17/17=17x/17` therefore `x=-1`

Explanation:

you firstly dissolve the denominator on the left side by multiplying with `5x+4` both sides. Then collect like terms, the once with the variable `x` on one side and one with real numbers on the other side. then solve to get the answer.