3rd Linear Inequalities & Systems of 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 (>, <, ≥, ≤) instead of an equal sign.

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 simultaneously.

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 (above or below the line) and use a dashed line for < or >, and a solid line for ≤ or ≥.

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 is a solution set in the context of inequalities?

Back

The solution set is the set of all points (x, y) that satisfy the given inequality or system of inequalities.

Front

How can you determine if a point is part of the solution set for a system of inequalities?

Back

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

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the specified number.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or equal to the specified number.

Front

What is the graphical representation of the inequality x < -1?

Back

The graphical representation of x < -1 is a dashed vertical line at x = -1, with the region to the left shaded.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the solution set from the non-solution set, indicating where the inequalities change from true to false.