Q2 Illuminate Practice

Front

What does the linear inequality 2x + 3y ≤ 12 represent in the context of budgeting?

Back

It represents the budget limitations by ensuring that the total spending on different categories does not exceed the budget.

Front

What is the linear inequality that represents the profit from producing x units of Product X and y units of Product Y, given that each unit of X gives a profit of $7 and each unit of Y gives a profit of $10, with a minimum profit of $350?

Back

7x + 10y ≥ 350

Front

How can the scenario of a company wanting to earn a minimum profit of $250 by producing e units of Product E (profit of $7 each) and f units of Product F (profit of $11 each) be represented as a linear inequality?

Back

7e + 11f ≥ 250

Front

If a bakery wants to earn at least $150 from selling Pastry A (profit of $4 each) and Pastry B (profit of $7 each), what is the linear inequality representing this situation?

Back

4a + 7b ≥ 150

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (like <, >, ≤, or ≥).

Front

What does the symbol '≥' mean in a linear inequality?

Back

It means 'greater than or equal to', indicating that the value on the left side is either greater than or equal to the value on the right side.

Front

What does the symbol '≤' mean in a linear inequality?

Back

It means 'less than or equal to', indicating that the value on the left side is either less than or equal to the value on the right side.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >), then shade the region that satisfies the inequality.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation shows equality (e.g., y = mx + b), while a linear inequality shows a range of possible values (e.g., y < mx + b).

Front

What is the feasible region in the context of linear inequalities?

Back

The feasible region is the area on a graph where all the constraints of the linear inequalities are satisfied.