Exploring Linear Absolute Value Equations and Inequalities

What is the definition of absolute value?

• The distance a number is from zero

• The distance a number is from its opposite

• The distance a number is from infinity

• The distance a number is from one

If the absolute value of x is 7, what are the possible values of x?

• 0 and -7

• 7 and 0

• 7 and -7

• 7 and 14

When solving |x - 1| < 5, what is the range of x?

• x is between -5 and 5

• x is between -6 and 4

• x is between -4 and 6

• x is between -3 and 7

What does it mean if an absolute value inequality is greater than a number?

• The values are closer to the center

• The values are further away from the center

• The values are exactly at the center

• The values are equal to zero

What is an extraneous solution?

• A solution that does not satisfy the original equation

• A solution that is always negative

• A solution that satisfies the original equation

• A solution that is always positive

Why can an absolute value never equal a negative number?

• Because absolute value represents a distance, which can be either positive or negative

• Because absolute value represents a distance, which is always negative

• Because absolute value represents a distance, which is always zero

• Because absolute value represents a distance, which is always non-negative

What is the central location in an absolute value inequality?

• The average of the boundary points

• The lowest boundary point

• The highest boundary point

• The midpoint between the boundary points

How do you determine the distance from the central location to each boundary point?

• Subtract the central location from the boundary point

• Multiply the central location by the boundary point

• Divide the central location by the boundary point

• Add the central location to the boundary point

What does the inequality |x - 14| > 7 represent?

• Values of x that are exactly 7 units away from 14

• Values of x that are less than 7 units away from 14

• Values of x that are more than 7 units away from 14

• Values of x that are exactly 14 units away from 7

In the inequality |x - 1| ≤ 5, what does the '≤' symbol indicate?

• Values of x are within 5 units of 1

• Values of x are more than 5 units away from 1

• Values of x are exactly 5 units away from 1

• Values of x are less than 1 unit away from 5