Exploring Absolute Value Inequalities

Why is it important to isolate the absolute value before solving an inequality?

• To eliminate variables

• To simplify the equation

• To determine if it is an 'and' or 'or' problem

• To make the inequality positive

What does the inequality |x| < 5 represent?

• All real numbers whose distance from 0 is greater than 5

• All real numbers greater than 5

• All real numbers less than 5

• All real numbers whose distance from 0 is less than 5

How can you remember if an absolute value inequality is an 'and' problem?

• If the inequality is equal to

• If the absolute value is isolated

• If the inequality is less than

• If the inequality is greater than

What does the inequality |x| > 5 represent?

• All real numbers greater than 5

• All real numbers less than 5

• All real numbers whose distance from 0 is less than 5

• All real numbers whose distance from 0 is greater than 5

What are the two changes you need to make when splitting an absolute value inequality?

• Change the variable and the number

• Change the variable and flip the sign

• Flip the sign and change the number to negative

• Flip the sign and change the number to positive

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

• Graph the solution

• Isolate the absolute value

• Split the inequality

• Flip the sign

When graphing the solution to |x| < 2, what should the graph look like?

• Two open circles at -2 and 2 with shading outside

• Two closed circles at -2 and 2 with shading outside

• Two closed circles at -2 and 2 with shading in between

• Two open circles at -2 and 2 with shading in between

In the context of absolute value inequalities, what does the term 'inclusive' mean?

• The inequality is an 'and' problem

• The inequality includes the boundary values

• The inequality excludes the boundary values

• The inequality is an 'or' problem

How do you graph the solution to |x| > 3?

• Two open circles at -3 and 3 with shading in between

• Two closed circles at -3 and 3 with shading in between

• Two open circles at -3 and 3 with shading outside

• Two closed circles at -3 and 3 with shading outside

If a pediatrician recommends a baby's bath water to be 95°F with a variance of 3°F, what is the acceptable temperature range?

• 92°F to 98°F

• 90°F to 100°F

• 91°F to 99°F

• 93°F to 97°F