Graphing inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

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

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is any number greater than 3.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. For example, y ≥ 2 means y is any number greater than or equal to 2.

Front

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

Back

The symbol '<' means 'less than'. For example, x < 5 means x is any number less than 5.

Front

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

Back

The symbol '≤' means 'less than or equal to'. For example, y ≤ 4 means y is any number less than or equal to 4.

Front

How do you graph the inequality y > x + 1?

Back

To graph y > x + 1, draw a dashed line for y = x + 1 and shade the area above the line.

Front

How do you graph the inequality y ≤ -3?

Back

To graph y ≤ -3, draw a solid line at y = -3 and shade the area below the line.

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 >).

Front

What does it mean if a point lies in the shaded region of a graph of an inequality?

Back

If a point lies in the shaded region, it is a solution to the inequality.

Front

What is the solution set of the inequality y < 2x + 3?

Back

The solution set includes all points below the line y = 2x + 3, which is represented by a dashed line.