Algebra Tutorials!
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Inequalities

Statements that express the inequality of algebraic expressions are called inequalities. The symbols that we use to express inequality are given below with their meanings.

## Inequality Symbols

 Symbol Meaning < Is less than ≤ Is less than or equal to > Is greater than ≥ Is greater than or equal to

It is clear that 5 is less than 10, but how do we compare -5 and -10? If we think of negative numbers as debts, we would say that -10 is the larger debt. However, in algebra the size of a number is determined only by its position on the number line. Fow two numbers a and b we say that a is less than b if and only if a is to the left of b on the number line. To compare -5 and -10, we locate each point on the number line (see figure below). Because -10 is to the left of -5 on the number line, we say that -10 is less than -5. In symbols,

-10 < -5.

We say that a is greater than b if and only if a is to the right of b on the number line. Thus we can also write

-5 > -10.

The statement a ≤ b is true if a is less than b or if a is equal to b. The statement a ≥ b is true if a is greater than b or if a equals b. For example, the statement 3 ≤ 5 is true, and so is the statement 5 ≤ 5.

Example

Inequalities

Determine whether each statement is true or false.

a) -5 < 3

b) -9 > -6

c) -3 ≤ 2

d) 4 ≥ 4

Solution

a) The statement -5 < 3 is true because -5 is to the left of 3 on the number line. In fact, any negative number is less than any positive number.

b) The statement -9 > -6 is false because -9 lies to the left of -6.

c) The statement -3 ≤ 2 is true because -3 is less than 2.

d) The statement 4 ≥ 4 is true because 4 = 4 is true.