An Inequality is a comparison between two or more things.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
For example, let’s take a bottle of water and a used car.
The bottle of water costs $1, and the car costs $20,000. Instinctively, we know that the car costs more than the bottle of water.
This relationship can easily be represented using Inequality Symbols:
Relating two expressions using Inequalities
In this lesson, we’re going to learn how to Solve Linear Inequalities so that the relationship between two or more numbers is clearly represented on a number line.
What’s so great is that solving linear inequalities is just like solving equations – get the variable by itself!
Furthermore, we will still be using all of our sure-fire techniques: SCAM!
But there is a warning…
…whenever we multiply or divide both sides by a negative number, we must flip the inequality symbol.
Why?
It has everything to do with the number line.
When we compare two positive numbers, it’s pretty obvious which one is greater than and which one is less than, just by looking at which number is bigger than the other.
Comparing Values of Numbers on the Number Line
But when we compare two negative numbers, things can get a little tricky. Picture a number line.
To the right are positive numbers and to the left are negative numbers.
Now, as we know, numbers are positioned so that as we progress from left to right the values get bigger.
That means, that if we are comparing two negative numbers together, the value that is closest to zero is bigger.
Consequently, to compare two numbers using inequality symbols, we must always account for their orientation on the number line, and therefore, we must “flip” our thinking when it comes to negatives.
Compound Inequalities
Don’t worry, all will make sense after the lesson!
In fact, we are going to see how easy it is to solve linear inequalities and graph the solution on a number line.
We will also look at how to solve Compound Inequalities!
What’s that?
Well, most linear inequalities have two parts (i.e., left side and right side), a compound inequality has three parts, as Cool Math so nicely states.
All this means is that instead of comparing two things together, we’re going to compare (organize from least to greatest) three things!
Solving Linear Inequalities – Video
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