Linear Inequality Review

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 inequalities?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

What does the symbol '<' represent in inequalities?

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either larger than or equal to the value on the right side.

Front

What does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either smaller than or equal to the value on the right side.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid 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 make the inequality true, often represented as a shaded region on a graph.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

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 the shaded areas overlap.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the values that make the inequality an equation. Depending on whether the inequality is strict or non-strict, the line may or may not be included in the solution.