Which graph represents the solutions of the inequality p ≥ -1

Option D:

The solution of the inequality p is –1, 0, 1, 2, 3, ...

Solution:

Given inequality is p ≥ –1.

To find the solution for the inequality.

p ≥ –1 means the value of p is greater than or equal to –1.

That is p can be –1, 0, 1, 2, 3, ...

Now find which option is correct:

Option A:

In this inequality, the solution is –1, –2, –3, ...

–3 and –2 are less than –1.

But p is greater than –1.

So, it is not the solution of the inequality.

Option B:

In this inequality, the solution is 0, 1, –1, –2, –3, ...

Here 0 > –1 and 1 > –1 but –3 and –2 are less than –1.

So, it is not the solution of the inequality.

Option C:

In this inequality, the solution is 0, 1, 2, 3, ...

Here 1 > –1 , 2 > –1 and so on.

But 0 is also greater than –1. This is missing in the graph.

So, it is not the solution of the inequality.

Option D:

In this inequality, the solution is –1, 0, 1, 2, 3, ...

Here –1 = –1, 0 > –1, 1 > –1,  and so on.

This graph represents all the values of p.

So, it is the solution of the inequality.

Hence option D is the correct answer.

The solution of the inequality p is –1, 0, 1, 2, 3, ...

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.