Now that we have reviewed how to solve some of the basic types of equations, it’s now time to look at Solving Inequalities.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
An Inequality is a mathematical sentence that uses greater than, less than, is not equal to, etc., and solving them is very similar to how we solve equations.
The solution to an equation or inequality is any number that, when plugged into the equation or inequality, will satisfy the equation or inequality.
In fact, the steps for solving an equation and solving an inequality are the same in the sense that whatever we do to one side of the equation or inequality, we must do to the other side, as nicely demonstrated by Math is Fun.
So what’s the difference?
When we solve an inequality, we must keep track of our negative signs! Because if we are multiplying or dividing both sides by a negative number we must change the direction of the inequality.
Okay, that’s easy…
…Is there anything else I need to know?
Yes!
Graph of a Linear Inequality
When you write your solution, you will need to use Interval Notation!
Interval Notation, as we discovered in our study of Trigonometry, is the preferred method of expressing intervals and inequalities because it’s easy to read and is more precise. So in this lesson, we will quickly review how to use Interval Notation and apply it to all of our solutions sets.
The types of Inequalities we are going to look at during this lesson are:
- Linear Inequalities
- Quadratic Inequalities
- Rational Inequalities
What’s so cool about this lesson is that it really sets us up perfectly for when we talk about Domain and Range, and how to represent and graph Polynomial Function and Rational Functions; major components of Calculus!
Solving Inequalities – Video
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