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'. It 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'. It indicates that the value on the left is smaller than the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Shade the appropriate region based on the inequality.

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 >).

Front

What does the inequality 0.85x + 375 > 450 represent?

Back

This inequality represents the condition that the total earnings of a limo driver, based on a rental fee and mileage, must be greater than $450.

Front

How do you solve the inequality 0.85x + 375 > 450 for x?

Back

To solve for x, subtract 375 from both sides to get 0.85x > 75, then divide both sides by 0.85 to find x > 88.24.

Front

What is the solution set for the inequality x < 5?

Back

The solution set for x < 5 includes all real numbers less than 5.

Front

What does it mean to shade a region in a graph of an inequality?

Back

Shading a region in a graph of an inequality indicates all the possible solutions that satisfy the inequality.

Front

What is a compound inequality?

Back

A compound inequality consists of two or more inequalities joined by 'and' or 'or', representing a range of values.