Inequalities (Single)
In this introductory inequality video course, you will first learn what inequalities are and how they differ from a normal equation. The course then explains how to represent inequalities on a number line. Next, you will learn the step-by-step method to solve simple inequality equations. Finally, the course introduces a special case where the coefficient of the variable is negative, and you will learn two effective methods to handle this situation correctly.
Related Lessons:
What Is Inequalities?
There are 4 inequality signs:
- < less than
- ≤ less than or equal to
- > more than
- ≥ more than or equal to
What Is A Number Line?
On a number line, we use two types of circles: an open circle and a filled (dark) circle. A filled circle is used when the inequality symbol includes an equal sign:
- open circle – for “less than” or “greater than”
- dark circle – for “less than or equal to” or “greater than or equal to”
Solving Inequalities Equation
When solving inequality equations, ensure that the coefficient of the variable is positive. In this scenario, the inequality equation can be solved in the same way as a linear algebraic equation. For example:
\(3x-5\le x-1\)
\(3x-x\le-1+5\)
\(2x\le4\)
\(x\le\frac{4}{2}\)
\(x\le2\)
Solving Inequalities Equation With Negative Coefficient
Unlike solving linear algebraic equations, when solving inequality equations the coefficient of the variable must be positive.
If the coefficient of the variable is negative, there are two methods we can use to handle this situation.
- Method 1: When dividing with a negative coefficient, we flip the inequality sign
- Method 2: We will perform a “flip all” to convert the algebraic negative coefficient to positive coefficient
The “flip all” method is preferred as it is a more direct and straightforward method. Let us go thru the “flip all” method:
\(-5x<8-x\)
\(-5x+x<8\)
\(-4x<8\)
We perform a “flip all” here:
\(4x>-8\)
Now that the coefficient of the algebra is positive, we can solve the inequality equation normally:
\(x>\frac{-8}{4}\)
\(x>-2\)