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One-fourth of the square root of 9 less than a number is 3. What is the number?  

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t4trendesetter | (Level 1) Honors

Posted February 26, 2013 at 7:13 PM via web

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One-fourth of the square root of 9 less than a number is 3. What is the number?

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 26, 2013 at 7:21 PM (Answer #1)

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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

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tjjavid | Student, Undergraduate | (Level 1) Honors

Posted February 26, 2013 at 7:27 PM (Answer #2)

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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

why are the answers negative?

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Wilson2014 | eNotes Employee

Posted February 27, 2013 at 11:47 PM (Answer #3)

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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 -15/4

why 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.  

             

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