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Why do you set up two absolute value equations?
Like when you have the equation lx-3l= 7 and you have to set up lx-3l equal to 7 and -7. I thought an absolute value could never equal a negative number because a distance can not be negative. So can you explain why you would set it up that way??
3 Answers
- Anonymous8 years agoFavorite Answer
Because
lx-3l= 7 = |7| = |-7|
hence
x-3=7
or
x-3=-7
- ?Lv 58 years ago
An absolute value will never equal a negative number.
You don't set |x - 3| = -7
You need two cases
case 1
x - 3 > 0
then x - 3 = 7
x = 10 and when x = 10, x - 3 > 0, so this is consistent and is a
valid soluteion
case 2
x - 3 < 0
then -(x - 3) = 7
3 - x = 7
x = -4
and when x = -4, x - 3 < 0, so this is also consistent
thus x = 10 and x = -4 are valid answers.
The negative sign goes in front of the expression within the absolute value
symbols.
- 8 years ago
because it is addressing the fact that the answer must always be positive even if the x isnt, i prefer not to think about things like that and just accept them for what they are
