Download 6.6 Notes

LESSON 6.6 - Problem Solving and Inequalities
Goal: Write and solve multi-step inequalities to solve real-world problems.
EXAMPLE 1
Writing and Solving an Inequality
Go-Karts At a go-kart park, you can pay $6 for admission and $4 for each ride, or you can buy an allday pass for $25, which includes admission and unlimited rides. How many times would you have to
ride the go-karts so that buying an all-day pass is a better value than paying for each ride?
Solution
To decide how many times you would have to ride the go-karts so that buying an all-day pass is a
better value, write and solve an inequality.
Let x represent the number of go-kart rides.
Price of gokart ride

Number of
rides
+
Cost of allday pass
Write an inequality.
Solve the inequality.
Now You Try It:
Write an inequality. Then use your inequality to solve the following problem.
1) At a miniature golf course, you can pay $5 for admission and $2 for each round, or you can
buy an all-day pass for $17, which includes admission and unlimited rounds. How many
rounds would you have to play so that buying an all-day pass is a better value than paying for
each round?
EXAMPLE 2 - Translating Verbal Sentences
Write the sentence as an inequality.
a) 3 times the sum of a number and 2 is less than 36.
First decide which inequality symbol to use. Then substitute numbers, variables, and operation
symbols.
The phrase “is less than” means ________.
3 times the sum of a number and 2 is less than 36.
b) 6 times a number, minus 8 is no more than twice the number.
The phrase “is no more than” means _______.
6 times a number, minus 8 is no more than twice the number.
Now You Try It!
Write the sentence as an inequality. Let x represent the unknown number.
2) 8 times the difference of a number and 2 is at least 30.
3) The sum of a number and 5 is more than 4 times the difference of the number and 4.
EXAMPLE 3 - Writing and Solving an Inequality
Cell Phone Plans A cell phone company offers two calling plans.
Plan A: no monthly fee, $.14 per minute
Plan B: $5 monthly fee, $.04 per minute
How many minutes do you need to use each month so that Plan B is the better value?
Plan A cost
per minute

Number of
minutes
Plan B cost
per minute

Number of
minutes
+