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 morethan 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.

Nine more than 4 times a number is at least 30 plus 11 times the number.

b.

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.

Three times a number divided by 4 is no more than 5 plus twice the number

c.

SOLUTION

First decide which inequality symbol to use. Then substitute numbers, variables, and operation symbols.

The phrase “is no more than” means ≤.

ANSWER The inequality is ≤ 5 + 2x.3x4

GUIDED PRACTICE for Examples 1, and 2

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?

1.

ANSWER

You would have to attend 10 or more games to make buying a season ticket the better value.

GUIDED PRACTICE

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.

for Examples 1, and 2

ANSWER The inequality is x – 4 < 3x + 10.

GUIDED PRACTICE

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.

for Examples 1, and 2

ANSWER The inequality is 6(x + 8) ≤ 2x – 12.