Inequalities, Solutions and Systems of Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does it mean for an ordered pair to be a solution to an inequality?

Back

An ordered pair (x, y) is a solution to an inequality if, when substituted into the inequality, the statement is true.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all ordered pairs that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the region that satisfies the inequality.

Front

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

Back

A strict inequality uses < or >, meaning the values cannot be equal. A non-strict inequality uses ≤ or ≥, allowing for equality.

Front

What does the solution set of an inequality represent?

Back

The solution set of an inequality represents all the ordered pairs (x, y) that make the inequality true.

Front

How can you determine if an ordered pair is a solution to a system of inequalities?

Back

Substitute the ordered pair into each inequality in the system. If it satisfies all inequalities, it is a solution.

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line indicates the limits of the solution set. Points on the line may or may not be included in the solution, depending on whether the inequality is strict or non-strict.

Front

What is a feasible region in the context of systems of inequalities?

Back

The feasible region is the area on a graph where all the inequalities in a system overlap, representing all possible solutions.

Front

How do you test if a point is in the solution set of an inequality?

Back

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