Systems of Inequalities

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 region where the graphs of the inequalities overlap.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Tags

CCSS.6.EE.B.8

Front

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

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Tags

CCSS.6.EE.B.8

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either larger than or equal to the value on the right side.

Tags

CCSS.6.EE.B.8

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either smaller than or equal to the value on the right side.

Tags

CCSS.6.EE.B.8

Front

How do you graph the inequality x > -3?

Back

To graph x > -3, draw a vertical dashed line at x = -3. Shade the region to the right of the line, indicating all values greater than -3.

Tags

CCSS.HSA.REI.D.12

Front

How do you graph the inequality y < 2?

Back

To graph y < 2, draw a horizontal dashed line at y = 2. Shade the region below the line, indicating all values less than 2.

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

Tags

CCSS.HSA.REI.D.12

Front

How do you determine which region to shade for the inequality y < mx + b?

Back

To determine which region to shade, pick a test point not on the line (like (0,0)). If the inequality holds true for that point, shade the region that includes the test point.

Tags

CCSS.HSA.REI.D.12

Front

What is the solution to the system of inequalities?

Back

The solution to a system of inequalities is the set of all points that satisfy all inequalities in the system, represented by the overlapping shaded regions on the graph.

Tags

CCSS.HSA.REI.D.12