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 (>, <, ≥, ≤).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shown as a shaded region on one side of a boundary line.

Front

How do 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 strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line.

Front

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

Back

'>' means that the value on the left is greater than the value on the right, indicating that the solutions are above the boundary line.

Front

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

Back

'<'' means that the value on the left is less than the value on the right, indicating that the solutions are below the boundary line.

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 represents the solutions.

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What is a solution set in the context of linear inequalities?

Back

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

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 non-strict (≤ or ≥) and not included if it is strict (< or >).

Front

How can you test if a point is part of the solution set for a system of inequalities?

Back

Substitute the point into each inequality in the system. If it satisfies all inequalities, it is part of the solution set.