Understanding Absolute Value Inequalities

What does the absolute value represent in the context of inequalities?

• A number's position on the number line

• The distance of a number from zero

• The product of a number and its reciprocal

• The sum of a number and its opposite

When the absolute value of a variable is less than a number, what type of statement does it form?

• An 'or' statement

• An 'and' statement

• A 'but' statement

• A 'not' statement

What happens to the inequality sign when you multiply or divide by a negative number?

• It remains the same

• It switches direction

• It becomes an equality

• It disappears

In a 'greater than' absolute value inequality, what type of statement is formed?

• A 'but' statement

• An 'and' statement

• An 'or' statement

• A 'not' statement

What is the first step in solving an absolute value inequality?

• Isolate the absolute value expression

• Add a constant to both sides

• Subtract a constant from both sides

• Multiply both sides by zero

How do you determine the inequality for a salary that can differ by a certain amount from the average?

• Use a quadratic inequality

• Use an absolute value inequality

• Use a 'greater than' inequality

• Use a 'less than' inequality

What does the midpoint represent in the context of graphing absolute value inequalities?

• The difference between the endpoints

• The sum of the endpoints

• The average of the endpoints

• The product of the endpoints

In a graph of an absolute value inequality, what does the distance from the midpoint indicate?

• The product of all solutions

• The sum of all solutions

• The exact solution

• The range of possible solutions

What is the central value in an absolute value inequality graph?

• The endpoint with the largest value

• The lowest point on the graph

• The midpoint between two endpoints

• The highest point on the graph

How do you write an absolute value inequality for a graph with endpoints at 2 and -4?

• x + 1 > 3

• x + 1 < 3

• x - 1 < 3

• x - 1 > 3