Systems of Inequalities Word Problems

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the region where the shaded areas of the inequalities overlap.

Front

How do systems of equations differ from systems of inequalities?

Back

Systems of equations have specific solutions (one, none, or infinitely many), while systems of inequalities can have a range of solutions represented by shaded regions.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to a certain number.

Front

How can you represent a word problem as an inequality?

Back

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using variables and inequality symbols.

Front

What is the first step in solving a system of inequalities?

Back

The first step is to graph each inequality on the same coordinate plane to find the overlapping region that represents the solution.

Front

In the inequality 5x + 10 ≥ 100, what does 'x' represent?

Back

'x' represents the number of hours Joan needs to babysit to earn at least $100 for her calculator.

Front

How do you interpret the solution of a system of inequalities?

Back

The solution is interpreted as all the possible values that satisfy all inequalities in the system, often represented as a shaded region on a graph.

Front

What is the significance of the flat rate in a taxi fare problem?

Back

The flat rate is a fixed cost that must be added to the variable cost per mile to determine the total fare.

Front

How do you set up an inequality for a budget constraint?

Back

You express the total cost as less than or equal to the budget amount, using variables to represent quantities.

Front

What does the term 'shaded region' mean in the context of graphing inequalities?

Back

The shaded region represents all the possible solutions that satisfy the inequality, showing where the values of the variables can lie.