Question #ae753

Dividing by a fraction is the same thing as multiplying by its reciprocal. Using this and the given information, let's write an inequality, with x being equal to the rational number.

`x *2/-3 > 5`

This can also be written as

`(2x)/-3 > 5`

To simplify, multiply by `-3`. When multiplying by a negative number, the sign must be flipped.

`2x < -15`

Now divide by 2 to isolate x.

`x < -7.5`

So, any rational number less than -7.5 would be an answer. Some possible answers are -8, -27, and -85.

Let's call the number we are looking for `x`

Write an inequality to match the information.

A number, divided by `-3/2` must be greater than `5`

`x div -3/2 > 5" "larr` solve for `x`

`x /(-3/2) >5`

Multiply both sides by `-3/2` to cancel the division by `-3/2`.
Remember that the inequality sign must change if you multiply or divide by a negative value,

`x /cancel(-3/2) color(blue)(xxcancel(-3/2)) < 5 color(blue)(xx-3/2)`

`x < -15/2`

The number can be any value which is less than `7 1/2`

They can be integers or fractions.

Some possible values are: `7 1/3, 7 1/4, 7 , 6 1/2, 6 ....`