Some Helpful Tools
This section will cover the fundamentals and rules of one-step inequalities.
Greater Than or Less Than Sign
Inequalities use the greater than sign (>) or the less than sign (<) to show that
amounts in a math statement are not equal.
If you are multiplying or dividing by a negative number, change the direction of the inequality sign to make the statement true.
Example 1: x + 2 < 6
What value would the variable x represent to make this statement true?
By solving for x, we could answer this question. Since the inverse of addition is subtraction, we can subtract 2 from both sides to get x on the left side by itself.
If the inequality states that x + 2 is less than 6, then x would represent any value that is less than 4.
Example 2: x + 7 > 12
If the inequality states that x + 7 is greater than 12, then x would represent any value that is greater than 5.
Greater Than or Equal to Sign
Less Than or Equal to Sign
Multiplying or Dividing with Negative Numbers
Statements may contain the greater than or equal to sign (>).
Example: x > 10
This means that x can be 10 or greater than 10.
Statements may contain the less than or equal to sign (<).
Example: x < 15
This means that x can be 15 or less than 15.
Example: -12x < 24
Divide both sides by -12.
Change the less than sign to a greater than sign.
Here's why:
Suppose we were to keep the less than sign the same. Our statement would say that the variable x can represent any number less -2.
Let's say we choose the number -3. If we were to let x represent -3, our statement would not be true because 36 is not less than 24.
By changing our sign to greater than, we can choose any number that is greater than -2.
Let's say we choose -1, our statement would be true because 12 is less than 24.
Math: One-Step Inequalities - Tutorial
