Creating Inequalities in one variable

An inequality is a statement that 2 quantities are not equal. The quantities are compared by using the following signs:

Greater than: > Less than: <Greater than or equal to: ≥ Less than or equal to: ≤

When reading a word problem you need to remember the following:

At most or no more than means “≤”

At least or no less than means “≥”

We will start with creating a basic inequality.

Tom’s dad told him not to turn on the air conditioner unless the temperature is at least 80˚ F.

Turn on the AC when temperature is at least 80˚ Let t represent the temperature.

t ≥ 80˚This is the tricky part…You would probably think that is

supposed to be ≤ BUT at least means that the temperature can be 80˚ or greater than 80˚.

Katy has $650 in a savings account at the beginning of the summer. She wants to have at least $200 in the account by the end of summer. She withdraws $30 each week for food, clothes, and activities. How many weeks can Katy withdraw from her account?

Again at least means greater or equal to.Let w represent the number of weeks.

650 – 30w ≥ 200Start of summer Withdraws 30 each week At least End of summer

650 – 30w ≥ 200-650 -650 - 30w ≥ -450 Divide both sides by a negative 30. Remember to reverse the sign.

W ≤ 15 Katy can withdraw from her account for 15 weeks or less.

An airport shuttle charges a $2.50 flat rate in addition to $0.75 per mile. A couple has no more than $55 to spend on a ride. How many miles can the couple travel without exceeding their limit?

First remember that no more than actually means less than or equal to.Let m represent the number of miles.

.75m + 2.50 ≤ 55.00 - 2.50 ≤ -2.50 .75m ≤ 52.50 Divide both sides by .75 m ≤ 70

The couple can travel 70 miles or less before reaching their limit of $55.

Averages

Jaxon needs at least an 85% to keep his X-Box. His teacher gives 5 tests throughout the semester. His scores were 90, 72, 86, and 94. What score does he need on the fifth test?

On a final note……..

*Read through the entire problem*Look for key words that you will need to solve the problem*Identify your variable*Create your inequality*Solve your inequality*Label your answer