Linear Inequalities and Systems of 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 (>, <, ≥, ≤).

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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 shaded on one side of the boundary line.

Front

What is the difference between a solid line and a dashed line in the graph of an inequality?

Back

A solid line indicates that points on the line are included in the solution set (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you determine the solution set for a system of linear inequalities?

Back

The solution set for a system of linear inequalities is the region where the shaded areas of all inequalities overlap.

Front

What does the symbol '≥' mean in an inequality?

Back

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

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What does the symbol '≤' mean in an inequality?

Back

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

Front

How can you tell if a point is a solution to a linear inequality?

Back

A point is a solution to a linear inequality if it satisfies the inequality when substituted into the expression.

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

Back

The boundary line separates the solution set from the non-solution set and indicates the values that satisfy the inequality.

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more linear inequalities that are considered together.

Front

How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a boundary line, then shade the appropriate region based on the inequality.