Reasoning Inequalities

Question

What value is a solution of y + 7 ≥ 12 but is not a solution of y + 7 > 12?

Answer 1

The "reasoning" portion of this question is this:

   [1] "greater than or equal to" (≥) -- yes

   [2] "greater than" (>) -- no

 

For [1] "greater than or equal to" to be true and for [2] "greater than" to be false, the solution must be:  y + 7 equal to 12

   That means: 

      y + 7 = 12

       y = 5       [subtract 7 from both sides]

 

The "solution" to the problem is the value of the variable (y) that "solves" [1] (that is, makes [1] true), but does not "solve" [2] (that is, does not make [2] true).  So, y=5 is that value (the "solution").

Answer 2

y + 7 ≥ 12 ⇒ y ≥ 5, y = 5

y + 7 > 12 ⇒ y > 5, y ≠ 5