Solving inequalities is very much like solving equations, but when solving equations you try to find points, when solving inequalities you try to find intervals.

Let’s start with an example of a linear inequality:

If you remember the inequalities properties, mainly that multiplication or division by a negative number reverses the inequality, you should be fine.

Another example, absolute value inequality:

Absolute value, one more thing to pay attention to…

How to solve quadratic inequalities? First you bring the inequality to the standard form. You can factor it or use the quadratic formula, just like with quadratic equations, but then what? Finding the ranges is somewhat tricky, but once you get the hang of it, it is straightforward.

Let’s try to solve quadratic inequality:

Before you take a look at the steps, you can check the plot, that should give you an idea of where the graph satisfies the inequality, or what might be the range.

Now let’s take a look at the steps:

The table makes it more manageable, that wasn’t too bad, wasn’t it?

Until the next post,

Michal