This week in Precalc 11 about solving inequalities with number lines and factors.

If you have an inequality, such as , you start by factoring it, in this case getting .

Then, you find the zeros, which for this inequality are and . You then place those zeroes on a number line.

Afterwards, you match each factor up to a number line, and find out whether each of the three segments on the line created by the zeroes are positive or negative.

Next, you combine each of those number lines by figuring out the positives and negatives on the overall number line. For example, if the middle segment on the first line is positive and negative on the second one, you’ll end up with a negative in the middle segment of the overall number line, as a positive and negative equal a negative when multiplied.

Then, you figure out whether your answer needs to be positive or negative and select a number within whatever segment needed.

With that, you have your answer. In this case, it’s and .