Linear and Systems of Inequalities Review

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 such as <, >, ≤, or ≥.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system when substituted into them.

Front

What type of line is used when graphing a linear inequality with < or >?

Back

A dotted line is used when graphing a linear inequality with < or > to indicate that points on the line are not included in the solution set.

Front

What type of line is used when graphing a linear inequality with ≤ or ≥?

Back

A solid line is used when graphing a linear inequality with ≤ or ≥ to indicate that points on the line are included in the solution set.

Front

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the graphical representation of the inequality @@x ge -2@@?

Back

The graph is a vertical solid line at x = -2, with the region to the right shaded, indicating all x-values greater than or equal to -2.

Front

What does the inequality @@y ge -2@@ represent graphically?

Back

It represents a horizontal solid line at y = -2, with the region above the line shaded, indicating all y-values greater than or equal to -2.

Front

Back

The solution set includes all real numbers less than 3, represented graphically by a dotted vertical line at x = 3 with the left side shaded.

Front

How can you check if a point lies within the solution set of a system of inequalities?

Back

Substitute the point into each inequality in the system. If it satisfies all inequalities, then it lies within the solution set.

Front

What does the term 'feasible region' refer to in the context of linear inequalities?

Back

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