Question

|x+4|=|x-4| HELPPPPPPPPPPP

Answer 1

x = 0

Explanation:

Because |-4| = |4| = 4, then the only way x+4 can be -4 is if x=0, and the only way x-4 can be -4 is if x=0 as well. x can't be 4 for instance because then we have |8|≠|0|.

Answer 2

0

Explanation:

If x ≥ 4, then the equation simplifies to x+4 = x-4, which gives 8=0, which is not true. Therefore, there are no solutions in this case.

If x < -4, then the equation becomes -(x+4) = -(x-4), which simplifies to -x-4 = -x+4. Simplifying further gives -8 = 0, which is not true. Therefore, there are no solutions in this case either.

If -4 ≤ x < 4, then the equation becomes x+4 = -(x-4), which simplifies to 2x = 0. Therefore, x = 0 is a solution.

If we plug x = 0 back into the original equation, we can see that it works:

|0+4| = |0-4|,

which simplifies to 4 = 4.

Therefore, the solution to the equation |x+4|=|x-4| is x = 0.