Question

Which equation contains a value of n that should NOT be placed in the shaded region of the Venn diagram? A -3n = -9 c 2n = 8 3 - 2n = 4 D -3n = -6

Answer 1

The shaded region in the Venn diagram is "natural numbers"

Recall that the natural numbers are positive integers and start from 1.

`\N=1,2,3,4,5,6,7\ldots`

We are asked to identify which of the given options contains a value of n that does not belong to the natural numbers.

Let us simplify each of the given equations.

Option A:

`\begin{gathered} -3n=-9 \\ 3n=9 \\ n=(9)/(3) \\ n=3 \end{gathered}`

3 is a valid natural number so it does belong to the shaded region.

Option B:

`\begin{gathered} 2n=8 \\ n=(8)/(2) \\ n=4 \end{gathered}`

4 is a valid natural number so it does belong to the shaded region.

Option C:

`\begin{gathered} -2n=4 \\ n=(4)/(-2) \\ n=-2 \end{gathered}`

-2 is not a natural number, therefore, it does not belong to the shaded region.

Option D:

`\begin{gathered} -3n=-6 \\ 3n=6 \\ n=(6)/(3) \\ n=2 \end{gathered}`

2 is a valid natural number so it does belong to the shaded region.

Therefore, the equation in option C contains a value of n that should NOT be placed in the shaded region of the Venn diagram.