Absolute Value Equations

What is absolute value? Absolute value is the distance a point is away from zero on the number line. It is also sometimes called magnitude.

What is absolute value? There are 2 points for every given distance (except for zero) one in the positive direction and one in the negative direction.

The symbol for absolute value is two vertical lines | |. | | The symbol for absolute value is two vertical lines | |. Be careful that you don’t confuse them with parentheses, which are curvy ( )

The absolute value of + 5: | + 5 | = 5 | 5 | The absolute value of + 5: | + 5 | = 5 because the point + 5 is 5 units away from zero on the number line.

The absolute value of – 5: | - 5 | = 5 because the point - 5 is 5 units away from zero on the number line.

The meaning of absolute value How many numbers are 5 units away from zero on the number line? | x | = 5 There are 2 answers: both + 5 and - 5

Stuffing can either equal + 5 or – 5 Solve this equation! | x + 2| = 5 | stuffing| = 5 Stuffing can either equal + 5 or – 5 x + 2 = +5 | x + 2 = – 5 x = + 5 – 2| x = – 5 – 2 x = 3| x = -7

FIRST: Isolate the Absolute Value | x + 2|+ 7 = 15 | x + 2| = 15 – 7 |stuffing|= 8 Stuffing can either equal + 8 or – 8 x + 2 = +8 | x + 2 = – 8 x = + 8 – 2 | x = – 8 – 2 x = 6 | x = – 10

Whoa! Absolute value can never be negative! Answer is “No Solution” Trick question | x + 2|+ 7 = 5 | x + 2| = 5 – 7 |stuffing|= – 2 Whoa! Absolute value can never be negative! Answer is “No Solution”

Absolute Value Means distance from zero or “magnitude” Always positive or zero since it is a distance. Absolute value equations – isolate the absolute value Solve for both + and – on the right Expect 2 answers.