Understanding Absolute Value Inequalities

What is the first step to take when dealing with absolute value inequalities?

• Multiply both sides by a constant

• Combine all terms on one side

• Split the absolute value to find different amounts

• Add a constant to both sides

Why can an absolute value never be less than zero?

• Because it is always negative

• Because it is a variable

• Because it is always zero

• Because it represents a distance

When is an absolute value inequality true for all real numbers?

• When the absolute value is less than zero

• When the absolute value is greater than a negative number

• When the absolute value is equal to zero

• When the absolute value is less than a positive number

What happens if an absolute value inequality is less than zero?

• It has no solutions

• It has all real numbers as solutions

• It has multiple solutions

• It has a single solution

Which of the following is a scenario where an absolute value inequality has no solution?

• Absolute value is greater than zero

• Absolute value is less than or equal to a negative number

• Absolute value is greater than a positive number

• Absolute value is equal to zero

How do you determine if an absolute value inequality is an 'and' or 'or' statement?

• By checking if the inequality is greater than a negative number

• By checking if the inequality is equal to zero

• By checking if the inequality is less than a positive number

• By checking if the inequality is greater than or less than

What should you do if you encounter a negative number while solving an absolute value inequality?

• Ignore the negative sign

• Multiply by zero

• Add a positive number

• Flip the inequality sign

What is the final solution in a compound inequality problem?

• The sum of all solutions

• The union of all solutions

• The intersection of solutions

• The difference between solutions

Why is it important to graph compound inequalities?

• To calculate the sum of solutions

• To determine the difference between solutions

• To visualize the solutions

• To find the union of solutions

What happens when you divide an inequality by a negative number?

• The inequality becomes undefined

• The inequality sign remains the same

• The inequality becomes an equation

• The inequality sign flips