can you help with absolute value?

Question

ok, so can absolute value ever be negative? i thought it couldn't, but after recenty researching, i am really confused. If there is a variable inside an absolute value, will the value of it ever,never, or sometimes be negative?

ok, can it EVER be negative. if a variable is inside of the absolute value, can the RESULT ever be negative? i understand that the variable, lets say x, can be negative, but will the result ever be negative is my question.

ok, sorry, but what if this statement was said, "whenever an equation invloves a variable INSIDE the absolute value symbol, the equation has two solutions." , would that be true, false, or sometimes?

Answer 1

Hi,

When you take the absolute value of a number or of an expression inside the absolute value, the answer from the absolute value is NEVER negative. However, a variable inside the absolute value bars can have a negative number as its individual value.

|5| = 5

|-26|= 26

| x - 3| = 5 can be solved as both x - 3 = 5 and as x - 3 = -5.
For x - 3 = 5, you add 3 and get x = 8. This makes sense because |8 - 3| = |5| = 5
For the other solution, x - 3 = -5, add 3 to both sides and get
x = -2. So the variable can be negative inside the absolute value, even though the absolute value of the whole expression is positive. Checking it, | -2 - 3| = | -5| = 5.

I hope that helps you! :-)

Answer 2

If there is a variable inside an absolute value, it could be negative, but that's the input into the absolute value. The output is always positive as you already know.

What is sometimes confusing is the piecewise definition of absolute value. That is, |x| = x when x >=0 or |x| = -x when x<0. All this means in plain English is if you plug in a nonnegative value into the absolute value, the same exact value comes out (x in, x out). But if you plug a negative value into the absolute value, its OPPOSITE comes out (x in, -x out).

Edited to answer your updated question: Are there always two solutions? No, if the absolute value is equal to 0, there's only one solution, and if the absolute value equals a negaitve number, there are no solutions. Or, what if you had something like this? | (x^2 + 4)| = 6. You would set (x^2+4) = 6 or -6. But there is no real solution to equation (x^2+4) = -6. So it's very hard to make blanket statements. We can say "if it's a linear expression inside an absolute value and the absolute value is equal to a positive number, there will ALWAYS be 2 solutions!" Happy now? :-)

Answer 3

An absolute can NEVER be negative but the variable inside the bars of absolute value can be negative
-x^2-4 is always negativ but I -x^2-4 I =
x^2+4( ytou must change sign if the inside is negative) is positiv

Answer 4

That depends what you mean.
For the function
f(x) = | x |

Are you asking if x can be negative, or the *result* of f(x) is negative?

If you're asking if x can be negative, then the answer is yes; the absolute value function accepts *any* value.

If you're asking if f(x), the result of taking the absolute value, can be negative, then the answer is no. The function takes in a real number and spits out a real number greater than or equal to 0.

Answer 5

If there is a variable inside the absolute value, [-9], it is positive no matter what i.e. 9. But if there is a variable on the outside -[9] then it can be negative i.e. -9. If there is avariable both inside and out -[-9], then it is positive because 2 negatives cancel out. Hope it helped!

Answer 6

Absolute value is the distance from zero in either direction.It is never a negative number , and all operations inside absolute value are performed first so you never end up with negative value. If their is a negative sign out side absolute value it means your value will be negative.

Answer 7

The absolute value can never ever be a neative. When something ask for the absolute value its say how far away the number is from 0. For example -600, its absolute value would be 600. If there is a varible ex. -3x, the absolute value would be 3x.

Answer 8

abs(x) for any real value x will always be positive, or zero. There's no two ways about it.

Absolute value does not take the opposite of a number, it takes the distance from the 0 on the number line

Answer 9

sometimes
you can have abs(x)=2
x can be 2 or -2