algebraic inequalities & graphing on a number line

Solve each.

a. -3x = - 6

b. -3x > - 6

 

Equation VS. Inequality

 

    Though the two statements above are similar, they are also different.

 

    The first statement, -3x = - 6, is an equation, a statement of equality, a statement with the verb "is" or "equals". It says, "The product of -3 and a number is -6."

 

    The second statement, -3x > - 6, is an inequality. It says, "The product of -3 and a number is greater than -6."

 

    To learn how to solve equations see solve linear equation w/paper & pencil. After you have learned about solving equations, read this page.

 

Inequalities

 

    Consider each of the following inequalities written in symbols and in words.

-3x > - 6, "The product of -3 and a number is greater than -6."

-3x < - 6, "The product of -3 and a number is less than -6."

-3x > - 6, "The product of -3 and a number is greater than or equal to -6."

-3x < - 6, "The product of -3 and a number is less than or equal to -6."

 

    To solve the equation -3x = -6, one divides both sides by -3 and gets x = 2.

 

    To solve the inequations above, one divides both sides by -3 and "FLIPS THE RELATION SYMBOL" and gets the following results.

 

x < 2, "The number is less than 2."

x > 2, "The number is greater than 2."

x < 2, "The number is less than or equal to 2."

x > 2, "The number is greater than or equal to 2."

 

 

 

  When you multiply or divide an inequality by a negative number, you must "flip" the sign to make the statement true. This is the ONLY difference between solving an equation and solving an inequality. The text box below will explain why this is necessary.

 

 

 

The symbols [ and ] are used to indicate that the endpoint is included. The symbols mean the same as the filled-in circle.

The symobls ( and ) are used to indicate the endpoint is not included. The symbols mean the same as the hollow circle.

 

Inequalities are expressed in other ways. Each of these says the same thing.

a.) The set of all numbers such that the number is greater than 2.

 

b.) {x | x > 2}   

 

c.)

d.)

 

Vocabulary & Stuff

set    integers number line    multiples    is greater than graph paper

© April 10, 2002, March 2008, A. Azzolino www.mathnstuff.com/math/algebra/ainequ.htm