绝对值不等式求解：求解|x+3|+|x-4|<0中的未知数x

Let's walk through this problem clearly—absolute value inequalities can trip people up, but this one's actually straightforward once you remember a key rule about absolute values.

First, a critical reminder: for any real number (a), the absolute value (|a|) is always non-negative (meaning it's either 0 or positive, never negative).

Applying this to our inequality:

• (|x+3|) will be ≥ 0 no matter what real value (x) takes
• (|x-4|) will also be ≥ 0 for all real (x)

Now, think about adding two non-negative numbers together. If you add something that's at least 0 to another thing that's at least 0, their sum will always be at least 0. There's no scenario where this sum could be strictly less than 0—no matter what (x) you plug in.

Final Conclusion #

There are no real numbers (x) that satisfy the inequality |x+3| + |x-4| < 0. The solution set is the empty set, which we can denote as (\emptyset) (or simply state "no solution exists").

内容的提问来源于stack exchange，提问作者Pyr James