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 (>, <, ≥, ≤).

Front

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

Back

'≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to a specified number.

Front

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

Back

'≤' means 'less than or equal to', indicating that the value can be either less than or equal to a specified number.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≥ or ≤) or dashed line (for > or <). 2. Shade the region that satisfies the inequality.

Front

What is the solution set of a linear inequality?

Back

The solution set 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

Substitute the point's coordinates 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 (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

What is the graphical representation of y ≥ -3?

Back

A horizontal line at y = -3, with the area above the line shaded.

Front

What is the graphical representation of 5x + y ≤ -1?

Back

A line representing the equation 5x + y = -1, with the area below the line shaded.

Front

How do you identify the correct graph for a linear inequality?

Back

Look for the line that represents the boundary of the inequality and check which side is shaded based on the inequality symbol.