Question

For how many integer values of g is 6<3g<12 ?
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Answer 1

Answer:

2<g<4

Step-by-step explanation:

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Answer 2

Answer:

Only for $1$ integer value of $g$ is $6 < 3g < 12$.

Step-by-step explanation:

Consider the inequality as follows:

$6 < 3g < 12$

To find: Integer values of $g$ such that $g$ lies between $6$ and $12$.

Case1. For negative integer.

Suppose $g=-1$,

⇒ $6 < 3(-1) < 12$

⇒ $6 < -3 < 12$ which is not possible.

A $-ve$ integer cannot lie between $2$ $+ve$ integers.

Thus, for negative integer, inequality $6 < 3g < 12$ does not hold.

Case2. For positive integer.

1) For $g=1$,

⇒ $6 < 3(1) < 12$

⇒ $6 < 3 < 12$ which is not possible.

As the number $3$ cannot be greater than $6$.

2) For $g=2$,

⇒ $6 < 3(2) < 12$

⇒ $6 < 6 < 12$ which is not possible.

As the number $6$ must be equal to itself.

3) For $g=3$,

⇒ $6 < 3(3) < 12$

⇒ $6 < 9 < 12$ which is true.

4) For $g=4$,

⇒ $6 < 3(4) < 12$

⇒ $6 < 12 < 12$ which is not possible.

As the number $12$ must be equal to itself.

Observe that after $g=4$, the middle value in the inequality exceeds the number $12$, which makes the given condition false.

Case3. For integer $0$,

⇒ $6 < 3(0) < 12$

⇒ $6 < 0 < 12$ which is not possible.

As the number $0$ cannot be greater than $6$.

Therefore, only for $1$ integer value of $g$ is $6 < 3g < 12$.

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