You know that 2 is a larger number than 1, and you know that ‐2 is a smaller number than ‐1, so how do you show both of these statements to be true?

While an equation is a demonstration of two quantities equal to one another, inequalities demonstrate two quantities not equal to one another. This includes algebraic expressions. You can show this relationship of inequality in four ways:

*x* < 3 means the the value of *x* is less than 3 but cannot equal 3

*x* ≤ 3 means the the value of *x* can be any value less than 3 or the value of *x* can be 3

*x* ≥ 3 means the value of *x* is greater than or equal to 3; the value can be 3

*x* > 3 means the value of *x* is greater than 3 but cannot equal 3

**Keep in Mind**

- The definition of the inequality sign refers to the value on the left hand side of the sign
- Think of the inequality sign as an open mouth that is always going towards the greater value (i.e. a person who is hungry will want the greater portion of food)
- You can also remember less-than because the less-than sign (<) is shaped like a slanted “L.”

Showing or graphing inequalities on a number line isn’t very different from showing a value on a number line. The only difference is that an inequality will have many solutions.

**A trick to remember which way to draw the arrow is to look at the inequality sign. The direction it is pointing creates an arrow for you.**

- What is the difference between
*x*≤ 6 and*x*< 6? - Graph
*x >*-3 on a number line. - Graph
*x*< 14 on a number line. - Graph
*x*≥ 7 on a number line. - Graph
*x*≤ -5 on a number line.

**Answers to Practice Problems**

- The first symbol, ≤, means that the value
*x*is less than 6 or equal to 6. The second symbol, <, means that the value*x*is less than 6 and cannot be equal to 6.

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