Question

Which graph represents the solution to the inequality 3 + 5/2x ≥ 2 − 132?

Answer 1

Option D.

Explanation:

We have the inequality:

3 + (5/2)*x ≥ 2*x - 13/2

First, let's try to isolate x in one side of the inequality:

3 + (5/2)*x ≥ 2*x - 13/2

(5/2)*x ≥ 2*x - 13/2 - 3

(5/2)*x - 2*x ≥ - 13/2 - 3

Now all the terms with an x are in the left, and the terms without are in the right.

We can rewrite this inequality as:

(5/2)*x - (4/2)*x ≥ - 13/2 - 6/2

(1/2)*x ≥ -19/2

Now, multiplying both sides by 2 we get:

2*(1/2)*x ≥ (-19/2)*2

x ≥ - 19

So the graph will be a solid point in x = -19, and a ray that extends to the right (the values that are larger than -19)

The correct option is the last graph, option D.