Question

Use complete sentences to describe the process in proving that the solution of an inequality is valid.

Answer 1

≥The solution of an inequality is an interval, i.e. a range.

To prove that the interval found as solution, you must consider several cases.

1) In the case that the ineguailty is ≥ or ≤, first use the limits of the interval to prove they are valid solutions. This is, replace the limit values, one at a time, and verifiy the inequality.

2) If the sign is ≥ or > use a value to the right of the limit value to show that the values to the right are solution, and use a value to the left to show that they are not solution.

3) If the sign is ≤ or <, use a value to the left of the limit value to show that it is a solution and a value to the right of the limit value to show that it is not a solution.