Inequalities and Real-World Applications

Front

What is a linear inequality?

Back

Front

How do you graph a linear inequality?

Back

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

Front

What does it mean for a solution to be 'at least' a certain value?

Back

'At least' means that the value can be equal to or greater than the specified amount. For example, if a person needs at least $200, they can have $200 or more.

Front

How do you write an inequality for a situation involving savings?

Back

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you determine the feasible region for a system of inequalities?

Back

To determine the feasible region, graph each inequality on the same coordinate plane and identify the area where all shaded regions overlap.

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness of the line and the direction of the inequality. A positive slope means the line rises, while a negative slope means it falls.

Front

How do you interpret the solution of a linear inequality?

Back

The solution of a linear inequality represents all the possible values of the variables that satisfy the inequality. It can be expressed as a range of values.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the points on the line are not included (< or >).

Front

How can you represent a real-world scenario with inequalities?

Back

To represent a real-world scenario with inequalities, identify the constraints and objectives, then translate them into mathematical expressions using inequalities.