Question

How do you solve `-2- \frac{3}{4} b = - \frac{11}{16}`?

Answer 1

`-2-\frac{3}{4}\cdotb=-\frac{11}{16}`

`-\frac{3}{4}\cdotb=-\frac{11}{16}+2`

`-\frac{3}{4}\cdotb=\frac{-11+32}{16}`

`-\frac{3}{4}\cdotb=\frac{21}{16}`

`b=\frac{21}{16}\cdot(-\frac{4}{3})`

`b=-\frac{7}{4}`

Answer 2

`b=-21/12=-7/4`

Explanation:

`"Note "3/4b=(3b)/4`

To eliminate the fractions in the equation multiply ALL terms on both sides by the `color(blue)"lowest common multiple"` ( LCM) of the denominators 4 and 16

The LCM of 4 and 16 is 16

`(16xx-2)-(cancel(16)^4xx(3b)/cancel(4)^1)=(cancel(16)^1xx-11/cancel(16)^1)`

`rArr-32-12b=-11larrcolor(red)" no fractions"`

add 32 to both sides.

`cancel(-32)cancel(+32)-12b=-11+32`

`rArr-12b=21`

divide both sides by - 12

`(cancel(-12) b)/cancel(-12)=21/(-12)`

`rArrb=-21/12=-7/4`

`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.

`-2-(3/4xx-21/12)=-2+21/16=-11/16`

`rArrb=-21/12=-7/4" is the solution"`