How many conditions should we know if we want to determine whether x > 6y?? (Inequalities question)

Question

My teacher gave me this question, but I don't know know to solve it.

Question:

How many conditions should we know if we want to determine whether x > 6y??

Condition 1: x >7y

Condition 2: x <9y

The answer is that we need both condition 1 and 2

Please tell me why ~~~~ Thanks

Answer 1

To “know the condition” means to know whether the inequality is TRUE or FALSE. For multiple conditions, we connect then using the logical operation AND.

FOR POSITIVE VALUES OF y:

If we know a single condition:

     If we know only that C-1 is TRUE, then C-3 (x > 6y) is TRUE.

     If we know only that C-1 is FALSE, then C-3 could be TRUE (6y-7y) or FALSE (less than 6y).

    If we know only that C-2 is TRUE, then C-3 could be TRUE (6y-9y) or FALSE (less than 6y).

    If we know only that C-2 is FALSE, then C-3 is TRUE.

So, FOR POSITIVE VALUES OF y, KNOWING ONE CONDITION is not enough to determine C-3.

If we know both C-1 AND C-2:

C-1      C-2       range   C-3

T          T          7y-9y    T

T          F          9y +      T

F          T          6y-7y   T

F F never n/a

NOW, draw the Number Line with negative value for y and rework the results.

Answer 2

If x > 7y, then certainly x > 6y, yet x < 9y in no way affects the truth of x > 6y.