Question

How do you solve `4= \frac { 2v + 1} { 4} - \frac { v - 3} { 8}`?

Answer 1

`v=9`

Refer to the explanation below for the process.

Explanation:

Solve:

`4=(2v+1)/4-(v-3)/8`

Multiply both sides by the least common denominator (LCD) `8`.

`8xx4=(color(red)cancel(color(black)(8^2))(2v+1))/color(red)cancel(color(black)(4^1))-(color(red)cancel(color(black)(8^1))(v-3))/color(red)cancel(color(black)(8^1))`

Simplify.

`32=2(2v+1)-(v-3)`

Expand.

`32=4v+2+v+3`

Simplify.

`32=3v+5`

Subtract `5` from both sides.

`32-5=3v`

Simplify.

`27=3v`

Divide both sides by `3`.

`27/3=v`

Simplify.

`9=v`

Switch sides.

`v=9`