Question

How do you solve `-5\frac { 2} { 3} - \frac { 3} { 4} b = - 4\frac { 5} { 12}`?

Answer 1

`b=-1 2/3`

Explanation:

`color(blue)(-5 2/3-3/4 b=-4 5/12`

First of all, simplify all of the mixed fractions (in the form of `x y/z`)

`rarr-17/3-3/4b=-53/12`

`rarr-3/4b=-53/12+17/3`

`rarr-3/4b=(-53+68)/12`

`rarr-3/4b=15/12`

`rarrb=cancel15^5/cancel12^3xx-cancel4^1/cancel3^1`

`color(green)(rArrb=-5/3=-1 2/3`

Hope that helps!!! ☺♠☻

Answer 2

`b = -1(2/3)`

Explanation:

Convert the individual terms to improper fractions.
`-17/3 -(3b)/4 = -(53)/12`
Taking 12 as L C M for L H S,
`(-68-9b)/cancel (12) = -53/cancel(12)`
`-9b = 68-53`
`b = -(15)/9 = -5/3 = -1(2/3)`

Answer 3

`b = -5/3`

Explanation:

Change all the fractions to improper fractions first:

`-5 2/3 -3/4b= -4 5/12`

`(-17)/3 -(3b)/4 = (-53)/12`

To get rid of the fractions, multiply each term by the LCD of the denominators (which is `12`)

`(-17color(blue)(xx12))/3 -(3bcolor(blue)(xx12))/4 = (-53color(blue)(xx12))/12`

Cancel the denominators and simplify

`(-17color(blue)(xxcancel12^4))/cancel3 -(3bcolor(blue)(xxcancel12^3))/cancel4 = (-53color(blue)(xxcancel12))/cancel12`

`-68 -9b = -53`

`-68+53 = 9b`

`" "-15 =9b`

`-15/9 =b`

`b = -5/3`