Solve for x: |x + 2| + 16 = 14 (absolute value equations)

Question

anonymous · Answer

$$\left| x \right| = 5 \implies x = + 5  or  x = -5$$

callisto · Answer

No solution?!
 |x + 2| + 16 = 14
Subtract 16 from both sides
 |x + 2|  = -2   =>  Wrong!!!

anonymous · Answer

yepp :)

anonymous · Answer

how is -2 wrong?

callisto · Answer

Absolute value means the positive value of something..
Let say x=-1
|x| = |-1| =1
So, |x+2| should give a positive value... Now, it's negative, so, it's wrong :| At least no x-int. for it :|

callisto · Answer

See this: http://www.wolframalpha.com/input/?i=%7Cx+%2B+2%7C+%2B+16+%3D+14

anonymous · Answer

modulus always yields a positive value. thats how it is defined

anonymous · Answer

but wouldn't you take the absolute value of -2 and turn it to 2?

anonymous · Answer

no

anonymous · Answer

-2 doesnt hv a modulus. why would u put it there??

callisto · Answer

Not in this question at least
You've got
|x+2| = -2 
As I've said, after you use that sign, you should get a +ve value, now, it's negative. So, it's not true..

anonymous · Answer

modulus is on x+2 and not on -2

anonymous · Answer

oh! i see what i did wrong. Thanks

callisto · Answer

Welcome!~