One-fourth of the square root of 9 less than a number is 3. Let the number be X.

=> (1/4)*3 - X = 3 and (1/4)*(-3) - X = 3

=> X = -9/4 and X = -15/4

The value of the number can be -9/4 and -15/4why are the answers negative?

These negative answers are the only values that will make the equation true. It can be tested out by substituting `-9/4` or `-15/4` for `X` and it can be seen that these values make the equation true. For example, taking `X=-9/4`

`(1/4)*sqrt(9)- X = 3=> (1/4)*sqrt(9) - (-9/4) = 3`

Subtracting a negative will yield a positive, which essentially means we can add the absolute value of that number.

`=> (1/4)3 + 9/4 = 3` `=> 3/4 + 9/4 = 3`

`=> 12/4 = 3`

`=> 3=3` which is true.

So -9/4 is the correct answers. Applying the concept, one can see that -15/4 is also a negative value that can make equation true when we are multiplying (1/4) by -3 instead of 3.

One-fourth of the square root of 9 less than a number is 3. Let the number be X.

`(1/4)*sqrt 9 - X = 3`

=> (1/4)*3 - X = 3 and (1/4)*(-3) - X = 3

=> X = -9/4 and X = -15/4

**The value of the number can be -9/4 and -15/4**