Solutions to Linear Inequalities

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 ≥) instead of an equal sign.

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, often visualized as a region on a graph.

Front

What is the difference between a solid line and a dotted line in graphing linear inequalities?

Back

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

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, then the point is part of the solution set.

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 of a linear inequality, it may or may not be included in the solution set, depending on whether the line is solid or dotted.

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 in the graph of a linear inequality.

Front

How can you graph a linear inequality?

Back

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

Front

What is the role of test points in solving linear inequalities?

Back

Test points are used to determine which side of the boundary line is part of the solution set by substituting the test point into the inequality.

Front

What is the solution to the inequality y > 2x + 1?

Back

The solution includes all points above the line y = 2x + 1, not including the line itself.

Front

What does it mean for a point to be 'not part of the solution set'?

Back

A point is 'not part of the solution set' if it does not satisfy the inequality when its coordinates are substituted into the inequality.