In short summary, solving inequalities is trying to find all values of x (typically) that satisfy the inequality.

In other words, we find all the numbers that work. Unlike an equation which usually has 1 or just a few answers, the answers to inequalities often involve an intervals worth of answers.

This section is meant as a review. Let me just highlight the basic types of problems:

• intersection of lines. Lok at example 2 in the book. The graphic shows the lines y = 1-(3x)/2 and y = x-4. Why do they graph these? Well to find solutions to the inequality, they graph the left side and right side and find where they intersect. The x value of the intersection solves the equality (when 1-(3x)/2 = x-4). The inequality then figures out which other x also work.
• Absolute value problems. For some reason, these are difficult! Keep in mind that an absolute value really has two inequalities with it. That is
  

  |x| < 3 and -3 < x < 3

  and
  

  |x| > 3 and x > 3 or x < -3

  mean the same thing. Read -3 < x < 3 as -3 < x and x < 3. Also, pay special attention to the role of and and or.

  Notice there are two types of answers depending on the inequality. Look at example 5 to see the first type.

• There are other types mentioned in the text, but these don't appear in the homework. You can skip these.