Retest Assignment for Inequalities/Sys. of Ineq.

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 a point to be a solution to an inequality?

Back

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

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 points that satisfy all inequalities in the system.

Front

How do you graph an inequality on a coordinate plane?

Back

To graph an 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 does the shaded region represent in a graph of inequalities?

Back

The shaded region represents all the possible solutions to the inequality or system of inequalities.

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What is the significance of the overlap in the shaded regions of a system of inequalities?

Back

The overlap in the shaded regions represents the solution set where all inequalities are satisfied simultaneously.

Front

How can you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the difference between a solution and a non-solution in the context of inequalities?

Back

A solution satisfies the inequality, while a non-solution does not satisfy at least one of the inequalities.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line, it is a solution if the inequality is ≤ or ≥; it is not a solution if the inequality is < or >.

Front

How do you identify a point that is NOT a solution to a system of inequalities?

Back

A point that is NOT a solution will fail to satisfy at least one of the inequalities when its coordinates are substituted.