[Math] Absolute value inequality $3 > |x + 4| \geq 1$

absolute valueinequality

I've just started with absolute value equations and I have a real hard time understanding how to solve this. I got the following question, and I can't make heads or tails out of it.

Assume that $x, y$ are points on the real line. Explain what $|x − y|$ means geometrically. Use this to illustrate the inequalities (as subsets of the real line) below and write the inequality without absolute values.

$3 > |x + 4| \geq 1$

All help will be much appreciated, even as much as small pointers will be more than welcome…

Best Answer

$|x-y|$ is the distance between $x$ and $y$ on a number line.

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