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 '>' represent in inequalities?

Back

The symbol '>' means 'greater than' and indicates that the value on the left is larger than the value on the right.

Front

What does the symbol '<' represent in inequalities?

Back

The symbol '<' means 'less than' and indicates that the value on the left is smaller than the value on the right.

Front

What does the symbol '≥' represent in inequalities?

Back

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

Front

What does the symbol '≤' represent in inequalities?

Back

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

Front

How do you graph the inequality y > 2?

Back

To graph y > 2, draw a dashed horizontal line at y = 2 and shade the area above the line.

Front

How do you graph the inequality y ≤ -3?

Back

To graph y ≤ -3, draw a solid horizontal 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 the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the points are not included ( < or >).

Front

How do you graph the inequality 2x + 3y < 6?

Back

First, convert to slope-intercept form (y < -2/3x + 2). Graph the line y = -2/3x + 2 with a dashed line and shade below the line.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true, often represented by a shaded region on a graph.