Use the information about music downloads on
page 499
to explain how rational equations are used to solve problems involving unit price. Include an explanation of why the actual price per download could never be $1.00.
8-6
Solving Rational Equations
and Inequalities
Main Ideas
• Solve rational
equations
• Solve rational
inequalities.
New Vocabulary
rational equation
rational inequality
GET READY for the Lesson
A music download service advertises
downloads for $1 per song. The
service also charges a monthly access
fee of $15. If a customer downloads x
songs in one month, the bill in dollars
will be 15 + . The actual cost per
song is 15 + X. To find how many
songs a person would need to
download to make the actual cost per
song $1.25, you would need to solve
the equation 15 7 * = 1.25.
Solve Rational Equations The equation 15+ * = 6 is an example of a
rational equation. In general, any equation that contains one or more
rational expressions is called a rational equation.
Rational equations are easier to solve if the fractions are eliminated. You
can eliminate the fractions by multiplying each side of the equation by the
least common denominator (LCD). Remember that when you multiply
each
side by the LCD, each term on each side must be multiplied by the LCD.
3
2 + 2
EXAMPLE Solve a Rational Equation
Solves + #2 Check your solution.
The LCD for the terms is 28(z + 2).
Original equation
28(2 + 2( 3 + 2) = 28(2 + 21 () Multiply each side by 204 + 2).
28(2 + 2)(3) +28(2+2)(32) = 28(3 + 2)(3) Distributive Property
1
(9z+18) + 84 = 212 +42 Simplify
92 + 102 = 212 +42 Simplity
Subtracts and 42 from
60 =122
each side.
5=2
Divide each side by 12
(continued on the next page)
lesson 8.6 Salve Rational Fouations and inequalities
479
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