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My question is:

Solve: $|x-4|< a$, where $a$ belongs to the real numbers. Solve this by considering various cases depending upon whether $a$ is negative, positive or zero.

What I have tried so far: If $a>0$ then: $x < a+4$ and $x>4-a$, if $a=0$ then there is no solution.

My doubt is: Should I consider the case $a<0$ as again $|x-4| which is not possible as absolute value cannot be negative.

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    Probably the hint should be: depending on whether $x-4$ is negative, positive, or zero.2019-01-14

1 Answers 1

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Hint: $|x-4| means that $x$ is closer than $a$ units to $4$.

Another Hint: $|x-4| means that $(x-4) and $-(x-4).

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    @Gerry: I see that in the link I provided, it says "In mathematics, the **absolute value** (or **modulus**)". I apologize for being so narrow-minded.2012-06-04