Page 151 - Algebra 1

Example
4
Solving Two-Step Equations with Fractions
Solve the equation. Then check the solution to see if it is reasonable.
_1 n - _1 = _3 234
SOLUTION
To isolate n, first eliminate the _1 and then eliminate the _1 . 32
Math Language
When you multiply a number by its reciprocal, the product is 1.
_2 ·_1 =1 12
_1 n - _1 = _3 234
+_1 = +_1 _ _3 _ _3
_1 n = _13 2 12
_2 · _1 n = _13 · _2 1 2 12 1
_ n = 13
Addition Property of Equality Simplify.
Multiplication Property of Equality Simplify.
6
Estimate toverifythatthesolutionisreasonable.
_13 is about 2. Substitute 2 for n. _1 of 2 is 1. 62
_1 subtracted from 1 is _2 , which is close to _3 . 334
So, the solution _13 is reasonable. 6
Application: Fitness
A gym charges a $90 fee plus $30 per month. Another gym charges a fee of $1500. How many years will it take for the charges at the first gym to reach $1500?
SOLUTION Write an expression to represent the total cost at the first gym. monthly cost times the number of months plus the membership fee
30 · x + 90
Use the expression to write an equation equal to the total cost of $1500. 30x + 90 = 1500
Example
5
Caution
Read the problem carefully. The number of months is unknown, but the question asks for the number of years.
136 Saxon Algebra 1
-_9_0 = -_9_0
30x = 1410
30 x = 1410 __
30 30 x = 47
Subtraction Property of Equality Simplify.
Division Property of Equality Simplify.
47 months is about 4 years. It will take about 4 years for the total charges at the first gym to reach $1500.