Algebra Tutorials! Monday 20th of January   Home Scientific Notation Notation and Symbols Linear Equations and Inequalities in One Variable Graphing Equations in Three Variables What the Standard Form of a Quadratic can tell you about the graph Simplifying Radical Expressions Containing One Term Adding and Subtracting Fractions Multiplying Radical Expressions Adding and Subtracting Fractions Multiplying and Dividing With Square Roots Graphing Linear Inequalities Absolute Value Function Real Numbers and the Real Line Monomial Factors Raising an Exponential Expression to a Power Rational Exponents Multiplying Two Fractions Whose Numerators Are Both 1 Multiplying Rational Expressions Building Up the Denominator Adding and Subtracting Decimals Solving Quadratic Equations Scientific Notation Like Radical Terms Graphing Parabolas Subtracting Reverses Solving Linear Equations Dividing Rational Expressions Complex Numbers Solving Linear Inequalities Working with Fractions Graphing Linear Equations Simplifying Expressions That Contain Negative Exponents Rationalizing the Denominator Decimals Estimating Sums and Differences of Mixed Numbers Algebraic Fractions Simplifying Rational Expressions Linear Equations Dividing Complex Numbers Simplifying Square Roots That Contain Variables Simplifying Radicals Involving Variables Compound Inequalities Factoring Special Quadratic Polynomials Simplifying Complex Fractions Rules for Exponents Finding Logarithms Multiplying Polynomials Using Coordinates to Find Slope Variables and Expressions Dividing Radicals Using Proportions and Cross Solving Equations with Radicals and Exponents Natural Logs The Addition Method Equations
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:

# Notation and Symbols

You have used many different notations and symbols in your study of mathematics, including exponential notation and ordering symbols. Here are some examples for you to review.

A positive integer exponent is used to indicate repeated multiplication of a number.

For example, the expression 73 is written in exponential notation. It means 7 Â· 7 Â· 7. The exponent is 3 and the base is 7.

Ordering symbols are used to indicate the relative position of two numbers on a number line. The number on the left is less than the number on the right.

For example, -4 is less than 2 because -4 lies to the left of 2. Symbol Meaning Example Position on Number line = is equal to Same position. ≠ is not equal to -4 ≠ 2 Different position. < is less than -4 < 2 -4 is to the left of 2. > is greater than 2 > -4 2 is to the right of -4. ≤ is less than or equal to -4 ≤ 2 -4 ≤ -4 -4 is to the left of 2.Same position. ≥ is greater or equal to 2 ≥ -4 -4 ≥ -4 - is to the right of -4.Same position.

Note

The pointed end of the inequality symbol always points towards the smaller number.

Thus, â€œfour is less than sevenâ€ is written 4 < 7.

Likewise, â€œseven is greater than fourâ€ is written 7 > 4.

Example 2

Which of the following statements are true?

a. -6 > -2

b. -5 < 3

c. 7 7

Solution

a. False. -6 > -2 is read â€œnegative six is greater than negative two.â€ This statement is false because -6 lies to the left of -2 on the number line. Therefore, -6 < -2.

b. True. -5 < 3 is read â€œnegative five is less than three.â€

This is true because -5 lies to the left of 3 on the number line.

c. True. 7 7 is read â€œseven is less than or equal to 7.â€ This means either â€œ7 is less than 7â€ or â€œ7 is equal to 7.â€ Since 7 = 7, the statement 7 7 is true. (An â€œorâ€ statement is true if either part is true.)

Note: The statement 7 ≥ 7 is also true.