Absolute Value And Inequalities

Question 0

What happens when a variable isn’t alone in the absolute value bars?

Answer 0

Must solve two equations for both negative and positive ranges

|p+2|=9
p+2=9 or p+2=-9
p=7 or p=-11

Question 1

What is absolute value?

Answer 1

The distance between a number and 0 on a number line, therefore always stated as positive. Used in situations that requires a range of numbers.

x=|3| means x=3 or x=-3

Question 2

What should be done if there are numbers outside the absolute value bars on the same side of the equation?

Answer 2

Get the absolute value part isolated first, then break equation into two parts for both positive and negative solutions.

Question 3

Absolute value inequalities become compound inequalities, two inequalities joined by AND or OR. What is the distinction between the two?

Answer 3

AND means both parts are true, OR means one or the other is true, but not necessarily both.

Ex |x|< x < 3 or x>-3 AND x<3

Question 4

Which type of absolute value inequality requires two inequalities?

Answer 4

Greater than or equal to. The first one sets the absolute value less than the negative value ; the other sets the absolute value greater than the positive value.

Question 5

Solve for m:

|6m|-2=42

Answer 5

m=7 or m=-7