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.
We are given the system of 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.