Question

Is the value of the fraction 7−2y/6 greater than the value of the fraction 3y−7/12 ?

For what values?(Make sure to use an inequality)

Answer 1

The value of the fraction
`(7-2y)/(6)` greater than the value of the fraction
`(3y-7)/(12)` for
`y<3.`

Explanation:

Find for which values the fraction
`(7-2y)/(6)` is greater than the fraction
`(3y-7)/(12).`

Solve the inequality:

`(7-2y)/(6)>(3y-7)/(12)`

Multiply it by 12:

`2(7-2y)>3y-7\\ \\14-4y>3y-7`

Separate variables and numbers:

`-4y-3y>-7-14\\ \\-7y>-21`

Divide by -7:

`y<3`

The value of the fraction
`(7-2y)/(6)` greater than the value of the fraction
`(3y-7)/(12)` for
`y<3.`