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 '≥' represent in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Front

How do you graph a linear inequality with a '>' or '<' sign?

Back

You graph a linear inequality with a '>' or '<' sign using a dashed line to indicate that points on the line are not included in the solution set.

Front

How do you graph a linear inequality with a '≥' or '≤' sign?

Back

You graph a linear inequality with a '≥' or '≤' sign using a solid line to indicate that points on the line are included in the solution set.

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, often represented as a shaded region on a graph.

Front

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

Back

A linear equation represents a straight line where the values are equal, while a linear inequality represents a region where the values are not necessarily equal, using inequality symbols.

Front

What does the graph of the inequality 'y < 3' look like?

Back

The graph of the inequality 'y < 3' is a horizontal dashed line at y = 3, with the area below the line shaded.

Front

What does the graph of the inequality 'x ≥ -2' look like?

Back

The graph of the inequality 'x ≥ -2' is a vertical solid line at x = -2, with the area to the right of the line shaded.

Front

How do you determine which side of the line to shade when graphing a linear inequality?

Back

To determine which side of the line to shade, you can test a point not on the line (usually (0,0)) in the inequality. If the inequality holds true, shade that side; otherwise, shade the opposite side.