Author: Kathy Halverson
Last saved by: MHE
Company: Halverson Household

Lesson 3-4

Example 1	Solve Equations by Dividing
Solve -3x = 27.  Check your solution and graph it on a number line.
   -3x = 27	Write the equation.
 = 	Divide each side by –3 to undo the multiplication in -3 ⋅ x.
  1x = -9	-3 ÷ -3 = 1, 27 ÷ -3 = -9
    x = -9	Identity Property; 1x = x

CHECK	    -3x = 27		Write the equation
	-3(-9)  27		Check to see whether this statement is true.
                                27 = 27  	The statement is true.

The solution is –9.  To graph the solution, draw a dot at –9 on a number line.

Real-World EXAMPLE 
Example 2	Use an Equation to a Solve Problem
MOVIES     It costs $7 per ticket to go to the movies.  If the total cost for a group of friends to go to the movies is $56, how many people are in the group?
Words	$7     times      the number of tickets      equals      the total cost.

Variables	Let x represent the number of tickets.

Equation	7           ·                          x                          =               56

  7x = 56	Write the equation.
 = 	Divide each side by 7.
    x = 8	Simplify.

CHECK       7x 	= 56		Write the equation.
                   7(8)	 56		Check to see whether this statement is true.
                      56 = 56	The statement is true.

Therefore, there were 8 people who went to the movies as a group.

Example 3	Solve Equations by Multiplying
Solve  = -3.  Check your solution and graph it on a number line.
        = -3			Write the equation.
 6 = (-3)6		Multiply each side by 6 to undo the division in a/6.
         a = -18			Simplify.
CHECK	    = -3		Write the equation.
	 -3	Check to see whether this statement is true.
	    -3 = -3  	The statement is true.
The solution is –18.  To graph it, draw a dot at -18 on a number line.