Download EXAMPLE 1 Writing and Solving an Inequality Season

EXAMPLE 1
Writing and Solving an Inequality
Season Tickets
Individual tickets for a college hockey game cost $8
each plus a one-time transaction fee of $5. You can
buy a season ticket for $99. How many games would
you have to attend so that buying a season ticket is a
better value than buying individual tickets?
SOLUTION
To solve the problem above, write and solve an
inequality. Let x represent the number of games.
EXAMPLE 1
Writing and Solving an Inequality
8x + 5 > 99
Write an inequality
8x > 94
Subtract 5 from each side.
x > 11.75
Divide each side by 8.
ANSWER
It doesn’t make sense to attend 11.75 games. So, you
would have to attend 12 or more games to make
buying a season ticket the better value.
EXAMPLE 2
Translating Verbal Sentences
Write the sentence as an inequality.
a. Six times the difference of a number and 3 is more
than 24
SOLUTION
First decide which inequality symbol to use. Then
substitute numbers, variables, and operation symbols.
The phrase “is more than” means >.
ANSWER
The inequality is 6(x – 3) > 24.
EXAMPLE 2
Translating Verbal Sentences
Write the sentence as an inequality.
b. Nine more than 4 times a number is at least 30 plus
11 times the number.
SOLUTION
First decide which inequality symbol to use. Then
substitute numbers, variables, and operation symbols.
The phrase “is at least” means ≥.
ANSWER The inequality is 9 + 4x ≥ 30 + 11x
EXAMPLE 2
Translating Verbal Sentences
Write the sentence as an inequality.
c. Three times a number divided by 4 is no more
than 5 plus twice the number
SOLUTION
First decide which inequality symbol to use. Then
substitute numbers, variables, and operation symbols.
The phrase “is no more than” means ≤.
3x ≤ 5 + 2x.
ANSWER The inequality is
4
GUIDED PRACTICE
for Examples 1, and 2
1. Basketball
Individual tickets for a college basketball game cost
$12 each plus a one-time transaction fee of $8. A
season ticket costs $125. How many games would you
have to attend so that buying a season ticket is a
better value than buying individual tickets?
ANSWER
You would have to attend 10 or more games to make
buying a season ticket the better value.
GUIDED PRACTICE
for Examples 1, and 2
Write the sentence as an inequality. Let x represent the
unknown number.
2. The difference of a number and 4 is less than 10
more than 3 times the number.
ANSWER
The inequality is x – 4 < 3x + 10.
GUIDED PRACTICE
for Examples 1, and 2
Write the sentence as an inequality. Let x represent the
unknown number.
3. Six times the sum of a number and 8 is no more
than 12 less than twice the number.
ANSWER
The inequality is 6(x + 8) ≤ 2x – 12.