Linear Inequalities Review

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 (>, <, ≥, ≤).

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system.

Front

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

Back

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 significance of the boundary line in a linear inequality?

Back

The boundary line represents the values where the inequality changes from true to false. Points on the line may or may not be included in the solution set depending on the inequality symbol.

Front

When is a boundary line solid?

Back

A boundary line is solid when the inequality includes 'equal to' (≥ or ≤).

Front

When is a boundary line dashed?

Back

A boundary line is dashed when the inequality does not include 'equal to' (> or <).

Front

What does the solution set of a linear inequality represent?

Back

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

Front

How can you graph a linear inequality?

Back

1. Graph the boundary line. 2. Use a solid or dashed line based on the inequality. 3. Shade the region that satisfies the inequality.

Front

What does it mean if a point lies above the boundary line in a graph of an inequality?

Back

If a point lies above the boundary line for a 'greater than' inequality, it is part of the solution set.

Front

What does it mean if a point lies below the boundary line in a graph of an inequality?

Back

If a point lies below the boundary line for a 'less than' inequality, it is part of the solution set.