Linear Inequalities and Systems of Linear Inequalities

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 (>, <, ≥, ≤).

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean in a linear inequality?

Back

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

Front

How do you graph a linear inequality?

Back

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

Tags

CCSS.HSA.REI.D.12

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

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more linear inequalities that are considered together.

Tags

CCSS.HSA.REI.D.12

Front

How do you find the solution set of a system of linear inequalities?

Back

To find the solution set, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a point is a solution to a system of linear inequalities?

Back

A point is a solution to a system of linear inequalities if it satisfies all the inequalities in the system.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the values where the inequality changes from true to false. Points on the line are included if the inequality is ≤ or ≥.

Tags

CCSS.HSA.REI.D.12

Front

How can you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality and check if the statement is true.