2 Variable inequality

Front

What is a two-variable inequality?

Back

A two-variable inequality is a mathematical statement that compares two expressions involving two variables, typically written in the form ax + by <, >, ≤, or ≥ c.

Front

How do you represent a budget constraint using a two-variable inequality?

Back

You can represent a budget constraint by forming an inequality that sums the costs of items multiplied by their quantities, ensuring the total does not exceed the budget.

Front

If apples cost $3 and oranges cost $2, how would you write an inequality for spending no more than $24?

Back

3x + 2y ≤ 24, where x is the number of apples and y is the number of oranges.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the left side can be less than or equal to the right side.

Front

What is the significance of the solution set in a two-variable inequality?

Back

The solution set represents all the possible pairs of values (x, y) that satisfy the inequality.

Front

How can you determine if a point is part of the solution set for a two-variable inequality?

Back

To determine if a point is part of the solution set, substitute the x and y values of the point into the inequality and check if the statement is true.

Front

What does it mean if a point (0, 4) is not part of the solution set for an inequality?

Back

It means that when you substitute x = 0 and y = 4 into the inequality, the resulting statement is false.

Front

How do you write an inequality to compare total costs of two different purchases?

Back

You can write an inequality by setting the total cost of one purchase greater than or less than the total cost of another purchase, depending on the context.

Front

What is the inequality that models the situation where the total fees from booths must be at least $3,700?

Back

85x + 200y ≥ 3700, where x is the number of small booths and y is the number of large booths.

Front

What does the symbol '>' indicate in an inequality?

Back

The symbol '>' indicates 'greater than', meaning the left side must be strictly larger than the right side.