Question

How do you solve `\frac { - 2x } { 3} = \frac { - 5} { 2} + \frac { - x + 1} { 3}`?

Answer 1

I gor `x=13/2`

Explanation:

I would first take a common denominator such as `6` and change the numerator accordingly to get:
`(2*(-2x))/6=(3*(-5)+2(-x+1))/6`
get rid of the denominators:
`(2*(-2x))/cancel(6)=(3*(-5)+2(-x+1))/cancel(6)`
rearrange and solve for `x`:
`-4x=-15-2x+2`
`2x=13`
`x=13/2`

Answer 2

`x=6 1/2`

Explanation:

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

`:.(-4x=-15+2(-x+1))/6`

`:.-4x=-15-2x+2`

`:.-4x+2x=-15+2`

`:.-2x=-13`

`:.-x=-13/2`

multiply L.H.S and R.H.S. by`color(red)-color(red)1`

`:.color(red)xcolor(red)=color(red)13/color(red)2`

`:.color(red)xcolor(red)=color(red)6color(red) 1/color(red)2`

substitute `color(red)xcolor(red)=color(red)(13)/color(red)2`

`:.(-2(color(red)13/color(red)2))/3=-5/2+(-(color(red)13/color(red)2)+1)/3`

`:.(-26/2)/3=-5/2+((color(red)-color(red)13/color(red)2)+1)/3`

`:.-cancel26^13/cancel2^1 xx 1/3=-5/2+(-6 1/2+1)/3`

`:.-13/3=-5/2+(-5 1/2)/3`

`:.-13/3=-5/2+((-11/2)/3)`

`:.-13/3=- 5/2+(-11/2 xx 1/3)`

`:.-13/3=-5/2-11/6`

`:.-13/3=(-15-11)/6`

`:.- 13/3=-cancel26^13/cancel6^3`
`:.-13/3=-13/3`

Answer 3

`x = 13/2`

Explanation:

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

When you have an equation with fractions you can get rid of the denominators by multiplying each term by the LCM of the denominators. In this case it is `6`

`(-2x xxcolor(blue)(6))/3 = (-5xxcolor(blue)(6))/2 +(color(blue)(6xx)(-x+1))/3`

cancel the denominators

`(-2x xxcolor(blue)(cancel6^2))/cancel3 = (-5xxcolor(blue)(cancel6^3))/cancel2 +(color(blue)(cancel6^2)(-x+1))/cancel3`

`-4x=-15 +2(-x+1)`

`-4x=-15-2x+2`

`15-2 = 4x-2x`

`13=2x`

`x= 13/2`