Solutions to Linear Inequalities

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 (>, <, ≥, ≤) instead of an equal sign.

Front

What does the solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality.

Front

How do you graph a linear inequality?

Back

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

Front

What is the significance of a dashed line in the graph of a linear inequality?

Back

A dashed line indicates that points on the line are not included in the solution set (for < or > inequalities).

Front

What does a solid line indicate in the graph of a linear inequality?

Back

A solid line indicates that points on the line are included in the solution set (for ≤ or ≥ inequalities).

Front

How can you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the difference between a solution set and a boundary line in linear inequalities?

Back

The solution set includes all points that satisfy the inequality, while the boundary line represents the points where the inequality becomes an equality.

Front

What does it mean if a point lies in the shaded region of a linear inequality graph?

Back

If a point lies in the shaded region, it means that the point satisfies the inequality and is part of the solution set.

Front

Can a point on the boundary line be part of the solution set?

Back

Yes, if the boundary line is solid (for ≤ or ≥), points on the line are included in the solution set. If the line is dashed (for < or >), points on the line are not included.

Front

What is the role of test points in solving linear inequalities?

Back

Test points are used to determine which side of the boundary line satisfies the inequality. By testing a point not on the line, you can identify the solution region.