Author: SEG
Last saved by: MHE
Company: McGraw-Hill

Lesson 1-5

Example 1	Solve an Equation
Find the solution of w – 6 = 3.  Is it 7, 9, or 12?

Replace w with each value.
 
Value for w | w – 6 = 3 | True or False?
7 | 7 – 6  3 | false
9 | 9 – 6  3 | true
12 | 12 – 6  3 | false

Therefore, the solution of w – 6 = 3 is 9.

Example 2	Solve an Equation
Multiple-Choice Test Item
Which value is the solution of 2 + 3x = 11?
A  6		B   4		C  3		D  1

Read the Test Item
The solution is the value that makes the equation true.

Solve the Test Item	Test each value.

  2 + 3x = 11					  2 + 3x = 11
2 + 3(6)  11		Replace x with 6.	2 + 3(4)  11		Replace x with 4.
         20  11					         14  11

   2 + 3x = 11					   2 + 3x = 11
2 + 3(3)  11		Replace x with 3.	2 + 3(1)  11		Replace x with 1.
         11 = 11  				           5  11
Since 3 makes the equation true, the answer is C.

Example 3	Translate Sentences into Equations
The sum of twelve and a number is nineteen.  Find the number.
Words		The sum of twelve and a number is nineteen.
Variables	Let n = the number.	Define the variable.
		The sum of twelve   and   a number 	is 	nineteen.
Equation	12 	 + 	n             = 	19

		12 + n = 19	Write the equation.
		12 + 7 = 19	Solve mentally:  Twelve plus what number is 19?
	                    n = 7	The solution is 7.

Miles 
(m)

Gallons of Gasoline (g)

20 | 1
40 | 2
80 | 4
120 | 6
Example 4	Use an Equation to Solve a Problem
MILAGE        A car can travel 20 miles on 1 gallon of gasoline.  The table shows the relationship between the number of miles traveled and the number of gallons of gasoline.
a.	Given g, the number of gallons, write an equation that can be used to find m, the number of miles.

Words		Number of miles is twenty times the number of gallons of gasoline.

Variables	Let m = number of miles.  Let g = number of gallons of gasoline.

Equation	m = 20g

b.	How many miles can the car travel on 12 gallons of gasoline?
m = 20g	Write the equation.
m = 20(12)	Replace g with 12.
m = 240	The solution is 240 miles.