Question

Choose the solution set represented by the following graph.

x R, x < -2
x R, x > -2
x
x R, x ≥ -2

Answer 1

Option A.

Explanation:

We need to find the solution set represented by the given graph.

From the given figure it is clear that there is an open circle around -2 and shaded region lie left side of -2.

Open circle around -2 represents that -2 is not included in the solution set.

Shaded area towards left of -2 represents that the solution must be less than -2. It means the sign of inequality is "<".

From the given graph it is clear that value of x lie in the interval (-∞,-2). So, the solution set is

`\text{Solution set}=\x`

Therefore, the correct option is A.

Answer 2

The solution set represented by the following graph is:

x∈ R, x < -2

Explanation:

Clearly from the figure we could see that the solution set is to the left of ' -2' and excluding the point '-2' since there is a open circle at -2.

This means that -2 is not included in the set.

Also in interval; form the set of points that belong to the solution set are:

(-∞,-2)

in set-builder form it is written as:

x