Solving and Graphing Inequalities

Front

What is an inequality?

Back

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

Front

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

Back

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

Front

How do you determine if an inequality should be graphed with a solid line?

Back

An inequality should be graphed with a solid line if it includes 'or equal to' in its symbol (≤ or ≥).

Front

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

Back

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

Front

What is the standard form of an inequality?

Back

The standard form of an inequality is typically written as Ax + By ≤ C, where A, B, and C are constants.

Front

How do you graph the inequality y ≥ mx + b?

Back

To graph y ≥ mx + b, first graph the line y = mx + b with a solid line, then shade the region above the line.

Front

What is the significance of the slope in the inequality y ≥ mx + b?

Back

The slope (m) indicates the steepness of the line and the direction it goes (upward or downward) as x increases.

Front

How can you represent a real-world situation with an inequality?

Back

You can represent a real-world situation with an inequality by identifying the constraints and relationships between variables.

Front

What is the meaning of the inequality 2.5x + 1.75y ≤ 20 in a real-world context?

Back

This inequality represents the total cost of x hot chips and y sodas being less than or equal to $20.

Front

How do you interpret the graph of an inequality?

Back

The graph of an inequality shows all the possible solutions that satisfy the inequality, with shaded regions indicating valid solutions.