Question

How do you solve `\frac { 1} { 2} - \frac { 9} { 4} v = - \frac { 3} { 4}`?

Answer 1

`v=5/9`

Explanation:

Begin by subtracting `1/2` from both sides.

`cancel(1/2-1/2)-9/4v=-3/4-1/2`

`-9/4v=-3/4-1/2`

Simplify the right side by finding the LCD, that is, `4`

`-9/4v=-3/4-1/2`

Multiply both the numerator and denominator of `1/2` by `2/2`

`-9/4v=-3/4-(1times2)/(2times2)`

`-9/4v=-3/4-2/4`

`-9/4v=-5/4`

Cross multiply: `(("top left" times "bottom right")/("bottom left"times "top right"))`

`-9vtimes4=-5times4`

`-36v=-20`

Divide by `-36` to both sides.

`cancel(-36)/cancel(-36)v=(-20)/-36`

`v=20/36`

Simplify the fraction. Both `20` and `36` are divisible by `4`

`v=(20divide4)/(36divide4)=5/9`

`v=5/9`