Linear Inequalities

Front

What is a linear inequality?

Back

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

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the values can be less than or equal to a certain number.

Front

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

Back

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

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 solution set of a linear inequality?

Back

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

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 solid line and a dashed line in graphing inequalities?

Back

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

Front

What is the graphical representation of the inequality y < 2x + 3?

Back

The graph will have a dashed line for y = 2x + 3, and the area below the line will be shaded.

Front

How do you solve a system of linear inequalities?

Back

To solve a system of linear inequalities, graph each inequality on the same coordinate plane and identify the region where all shaded areas overlap.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it is included in the solution set if the inequality is ≤ or ≥, but not included if the inequality is < or >.