Real-World Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does 'at least' mean in mathematical terms?

Back

'At least' indicates a minimum value that a variable can take. For example, if x is at least 5, then x ≥ 5.

Front

What does 'at most' mean in mathematical terms?

Back

'At most' indicates a maximum value that a variable can take. For example, if x is at most 10, then x ≤ 10.

Front

How do you represent a situation where a person needs to collect a minimum number of items?

Back

You can represent this situation using an inequality. For example, if Jo needs at least 1000 signatures and has 520, the inequality would be 520 + 6x ≥ 1000.

Front

What is the inequality for Carla's basketball score situation?

Back

To find out how many two-point baskets she needs to score at least 46 points, the inequality is 24 + 2x ≥ 46.

Front

How do you set up an inequality for Adam's earnings at work?

Back

If Adam earns $80 per day plus $8 per video game sold, and he wants to make at least $176, the inequality is 80 + 8x ≥ 176.

Front

What is the formula for the perimeter of an equilateral triangle?

Back

The perimeter P of an equilateral triangle with side length s is given by P = 3s.

Front

If the perimeter of an equilateral triangle is at most 45 cm, what is the maximum length of each side?

Back

If P ≤ 45 cm, then each side s must be at most 15 cm, since 3s ≤ 45.

Front

How do you express a situation where a savings account must not drop below a certain amount?

Back

You can express this with an inequality. For example, if Bryan has $800 and withdraws $35 each week, the inequality is 800 - 35x ≥ 150.

Front

What does it mean if a variable is bounded by an inequality?

Back

It means that the variable can only take on values within a certain range defined by the inequality.