Solving Absolute Value Inequalities in One Variable

What is the first step in solving absolute value inequalities?

• Isolate the absolute value

• Combine like terms

• Multiply both sides by a reciprocal

• Add the same number to both sides

What does 'more is or' mean in the context of absolute value inequalities?

• The solutions will overlap

• The solutions will be in between the numbers

• The solutions will be on the outsides of the graph

• The solutions will be equal to the numbers

If the absolute value inequality is less than a positive number, what type of solution do we have?

• Two solutions that overlap

• Infinite solutions

• No solution

• One solution

When solving the positive side of an absolute value inequality, what changes?

• The number on the right side

• The inequality symbol

• Both the inequality symbol and the number

• Nothing changes

What must you remember to do when multiplying or dividing by a negative number in an inequality?

• Add the same number to both sides

• Switch the inequality direction

• Subtract the same number from both sides

• Keep the inequality direction the same

What happens if the number after the inequality is negative?

• The absolute value must be isolated again

• The inequality must be rewritten

• There is either no solution or infinite solutions

• There are always two solutions

When is an absolute value always greater than a negative number?

• Always

• Only when the number is positive

• Sometimes

• Never

What is the solution when an absolute value is less than a negative number?

• All real numbers

• No solution

• Two solutions

• One solution

If the absolute value of x is greater than 18, what are the solutions?

• x is between -18 and 18

• x is less than -18 or greater than 18

• x is equal to 18

• x is greater than -18

What is the solution when the absolute value of x is less than -11?

• All real numbers

• x is less than -11

• No solution

• x is between -11 and 11