Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is less than, greater than, or equal to another.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be either less than or equal to the value on the right.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be either greater than or equal to the value on the right.

Front

How do you solve the inequality 2x < 8?

Back

To solve 2x < 8, divide both sides by 2: x < 4.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

Front

If a parking garage charges a base fee plus an hourly rate, how can you express the total cost as an inequality?

Back

Let x be the number of hours parked. The total cost can be expressed as: Total Cost = Base Fee + Hourly Rate * x. For example, if the base fee is $2.50 and the hourly rate is $4.00, the inequality would be: 2.50 + 4.00x ≤ Total Amount Available.

Front

How do you represent a situation where a total weight limit is given?

Back

You can represent it with an inequality. For example, if the total weight limit is 1000 pounds and the current weight is 675 pounds, you can write: 675 + x ≤ 1000, where x is the weight of an additional person.

Front

What is the solution to the inequality -4x ≥ 10?

Back

To solve -4x ≥ 10, divide both sides by -4 and flip the inequality sign: x ≤ -2.5.

Front

If a beekeeper sells jars of honey for $3.00 each and needs to make at least $43, how do you set up the inequality?

Back

Let j be the number of jars sold. The inequality would be: 3j ≥ 43.

Front

How do you find the maximum number of months you can afford a gym membership given a fixed budget?

Back

Set up an inequality based on the total cost. For example, if the membership costs $60 plus $40 per month, and you have at most $210, the inequality would be: 60 + 40m ≤ 210, where m is the number of months.