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: ≤ 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 “≥” 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 ≥ 200 Start of summer Withdraws 30 each week At least End of summer 650 – 30w ≥ w ≥ -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. Again at least means greater or equal to. Let w represent the number of weeks. 650 – 30w ≥ 200 Start of summer Withdraws 30 each week At least End of summer 650 – 30w ≥ w ≥ -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 ≤ ≤ m ≤ 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