Real world application for 27 is less than or greater than 4x-7

Question

Need a paragraph describing equation like there are 4 girls etc

Answer 1

Although math notations are much more concise and precise than most English word (story) problem statements, this one looks like:

    "A is less than or greater than B"

  which is (when expanded):

    "A is less than B  OR  A is greater than B"

 

In addition, we must understand that this is the Exclusive OR (that is, one or the other, but not both; sometimes written XOR) rather than the inclusive OR (that is, one or the other or both).  This is verified by the relations "less than" and "greater than" which cannot both be true.

 

So, we have:

   [a]  27 < 4x-7       OR      [b]  27 > 4x-7

 

Let's solve for x:

  [a]  27 < 4x-7

         34<4x     [add +7 to both sides retains the sense of the inequality]

         34/4 < x    [divide by +4 retains the sense of the inequality]

        x >17/2      [reduce and write like reading r-to-l]

 

  [b]  27 > 4x-7

        34>4x     [add +4 to both sides retains the sense of the inequality]

        17/2 > x     [divide by +4 retains the sense of the inequality]

        x < 17/2

 

All value of x, such that EITHER [b] x < 17/2  or else [a] x > 17/2 are "solutions" [that is. make these inequalities true] to these inequalities.

 

Now, looking at out original paraphrase of the problem:  "A is less than B  OR  A is greater than B"

   This is exactly the same as saying, "A is not equal to B"

      [note: this is an important rule to remember]

 

The solution to the problem is:   any x such that x ≠ 17/2

 

Note:   17/2 (improper fraction) = 8 1/2 (mixed number) = 8.50 (decimal value)

 

Sample problem:

  Q: If 4 girls ate the same meal at a restaurant, sharing the $7 tip, so that $27 was less than or greater than the total amount minus $7, what could the cost for each girl's meal have been?" 

  A:  Not $8.50; that is, less than or greater than $8.50