The values of a, b, and c do not matter, only think about the fact that c is less than 0.
First inequality: No solution. Second inequality: All real numbers.
Practice makes perfect
We are given two inequalities, let's look at them one at a time.
First inequality
The first inequality we are given is:
|ax+b|
where c<0. The constraint means that c can only be a negative value. We know that an absolute value, no matter what the expression inside simplifies to be, will always produce a positive result. Therefore, we can think about this absolute value inequality in general terms as:
positive number< negative number.
This will never be true, so there is no solution to this inequality.
Second inequality
The second inequality we are given is:
|ax+b|>c,
where c<0. The constraint means that c can only be a negative value. We know that an absolute value, no matter what the expression inside simplifies to be, will always produce a positive result. Therefore, we can think about this absolute value inequality in general terms as:
positive number> negative number.
This will always be true, so the solution set is all real numbers.
