Check the numbers that are in the solution set and some that are near but outside of it.
See solution.
Practice makes perfect
The solution of a linear inequality is an interval that contains infinitely many real numbers. This means that the solution set includes infinitely many elements. Since we cannot check infinitely many numbers — it is impossible to check all the numbers in the solution set. Let's now solve the given inequality!
The answer x ≥ 8 means that the solution set includes all numbers greater than or equal to 8. We are able to verify this solution by checking as few as three numbers.
We need to check that one number that is less than 8 does not satisfy the inequality.
We need to check that 8 satisfies the inequality.
We need to check that one number that is greater than 8 satisfies the inequality.
For simplicity, let's use 7 as our lesser number and 9 as our greater number. If our solution is correct, only numbers that are greater than or equal to 8 will make the given inequality true.
x
x-11 ≥ - 3
Simplify
True or False?
7
7-11 ? ≥ - 3
- 4 ≱ - 3
False
8
8-11 ? ≥ - 3
- 3 ≥ - 3
True
9
9-11 ? ≥ - 3
- 2 ≥ - 3
True
Substituting a number that is less than 8 produced a false statement. Substituting numbers that are greater than or equal to 8 produced true statements. Therefore, x≥ 8 is the correct solution.
