AFDA Linear Inequalities and Systems of 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 (>, <, ≥, ≤).

Tags

CCSS.7.EE.B.4B

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Tags

CCSS.6.EE.B.8

Front

What does the symbol '>' represent in inequalities?

Back

The symbol '>' means 'greater than', indicating that the value on the left is strictly greater than the value on the right.

Tags

CCSS.6.EE.B.8

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a linear inequality?

Back

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

Tags

CCSS.HSA.REI.D.12

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 (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities with the same variables. The solution is the region where the shaded areas of the inequalities overlap.

Tags

CCSS.HSA.REI.D.12

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 of an inequality, it may or may not be included in the solution set, depending on whether the inequality is strict or non-strict.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness of the line and the direction of the inequality. A positive slope means the line rises, while a negative slope means it falls.