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 (>, <, ≥, ≤).

Front

What does the solution set of a linear inequality represent?

Back

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

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, shade the region that satisfies the inequality.

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

Front

What does it mean for a point to be a solution to a linear inequality?

Back

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

Front

How can you determine if a point is part of the solution set for a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What is a system of linear inequalities?

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

Front

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

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To find the solution set, 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 separates the solution set from the non-solution set and indicates the values that satisfy the inequality.

Front

Can a point on the boundary line be part of the solution set?

Back

Yes, if the inequality is inclusive (≥ or ≤), points on the boundary line are part of the solution set.