what is the formula in solving absolute value inequalities?
2006-11-20 20:50:03 · 7 answers · asked by charles yves 1 in Science & Mathematics ➔ Mathematics
Use the definition
ie
|a| = a for a ≥ 0
= -a for a < 0
2006-11-20 21:22:28 · answer #1 · answered by Wal C 6 · 0⤊ 0⤋
There is no 'formula', but I guess you mean 'algorithm' or something like that.
Draw a number line. Every absolute value in the equation splits this up into two halves - the half where the thing inside the absolute value is positive, and the half where it is negative.
So, for each absolute value, you have divided the line in half somewhere. You end up with several segments of the line. Consider each of those segments one at a time; once you know what segment you are in, you know exactly what each part of the equation is equal to.
An example: |x|+|x+3| < 9.
The first one divides the number line into >=0 and <0. The second one divides it into >=-3 and <-3.
Thus, we have these possibilities:
Region 1, where x<-3. Then |x|+|x+3| = -x-x-3 = -2x-3<9, so -2x<12, so x>-6. Thus this part gives you all x in (-6,-3).
Region 2, where -3<=x<0. Then |x|+|x+3| = -x+x+3 = 3<9, so all x in [-3,0) work.
Region 3, where x>=0. Then |x|+|x+3|=x+x+3 = 2x+3<9, so 2x<6, so x<3, so all x in [0,3) work.
Overall, any x in (-6,3) works.
2006-11-20 20:57:45 · answer #2 · answered by stephen m 4 · 0⤊ 0⤋
there's no formula... you solve them the same way you'd solve any inequality, however you must isolate the absolute value, then take both the positive and negative values of the side not in the absolute value signs.
also, in reguards to the sign, a trick to remember if its AND or OR is less thAND and greatOR than
ie:
4 > |x|
4 > x OR -4 > x
4 < |x|
4 < x AND -4 < x
hope it helps :D
2006-11-20 20:57:59 · answer #3 · answered by ekimollidrac 3 · 0⤊ 0⤋
There is no formula for this
Consider you have two equations
If x>=0 you get solution set A
If x<0 you get solution set B
The complete solution is A U B
Th
2006-11-20 21:32:44 · answer #4 · answered by Thermo 6 · 0⤊ 0⤋
Its the same as solving equaliies except the > or < signs become reversed if you multiply or divide each side by a negative number.
2006-11-20 20:56:12 · answer #5 · answered by epbr123 5 · 0⤊ 0⤋
inqualities, hmmmm.....
such as a = a Dolphin, B = either a Shark or Gangleon or a bunch of planktoon, so that
a would be >>>>>>> B if a had zero-in on it at onze.
2006-11-20 21:17:11 · answer #6 · answered by Anonymous · 0⤊ 0⤋
For all x belong to real number, and that a is positive(ie strictly greater than zero):
|x| < a IS EQUIVALENT TO -a < x < a
2006-11-20 20:56:53 · answer #7 · answered by lim_jz 2 · 0⤊ 0⤋