# Find the correct description of the graph of the compound inequality x − 3 < −9 or x + 5 ≥ 10.

Inequalities are very important concepts that are required in calculating the domain or the range of a variable in any algebraic, trigonometric, or differential equation.

## Answer: The region represented by the given inequalities on the graph does not converge anywhere; hence, the given system of inequalities does not have any solution.

Let's understand in detail.

**Explanation:**

We are given the compound inequalities:

⇒ x − 3 < −9 (equation 1)

⇒ x + 5 ≥ 10 (equation 2)

We can rearrange equation 1 as:

⇒ x < 3 - 9

⇒ x < -6

We can rearrange equation 2 as:

⇒ x + 5 ≥ 10

⇒ x ≥ 10 - 5

⇒ x ≥ 5

Hence, we have the solutions as x < -6 and x ≥ 5.

Now, we can represent the above inequalities on the graph as shown below.

Here, x < -6 is represented by the red region on the left and x ≥ 5 is represented by the blue region on the right.

Now, from the graph above, we can see that the system of inequalities does not converge anywhere on the graph.

### Hence, the region represented by the given inequalities on the graph does not converge anywhere; hence, the given system of inequalities does not have any solution.

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