Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '>' represent in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is any number greater than 5.

Front

What does the symbol '<' represent in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 3 means x is any number less than 3.

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 4 means x is any number greater than or equal to 4.

Front

What does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 2 means x is any number less than or equal to 2.

Front

How do you graph the inequality y > 2x - 5?

Back

To graph y > 2x - 5, first graph the line y = 2x - 5 as a dotted line (since it's not inclusive), then shade the area above the line.

Front

What is the difference between a solid line and a dotted line in graphing inequalities?

Back

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

Front

How do you determine if a point is part of the solution set for an inequality?

Back

To determine if a point is part of the solution set, substitute the coordinates of the point into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

How do you graph the inequality y ≤ -x + 1?

Back

To graph y ≤ -x + 1, first graph the line y = -x + 1 as a solid line (since it's inclusive), then shade the area below the line.