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I'm not sure how to solve absolute values. How do I find the value of an absolute value.

Here are some examples: Does |-x+3| equal x-3? Does |x+3| equal x+3?

Ted
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user8143349
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  • you must do case work – Dr. Sonnhard Graubner Jun 11 '17 at 06:48
  • Without knowing the value of $x$ you can not find the value of it. I.e. you can not write it any simpler than you currently have it. Also using the word solve implies you have an equation. Is that what you meant when you said solve absolute values? If so please give an example of an equation using absolute value that you need help solving. – Ian Miller Jun 11 '17 at 06:51
  • Welcome to Math.StackExchange.com! Please show what have you already found and why were your findings insufficient. – William Phoenix Jun 11 '17 at 06:56
  • Well okay sorry I'm not a maths professor Ian Miller. What matter's is my final two questions as a matter of fact. – user8143349 Jun 11 '17 at 06:59

2 Answers2

2

we have $$|-x+3|=-x+3$$ if $$3\geq x$$ $$|-x+3|=-(-x)+3)=x-3$$ if $$3<x$$

Dr. Sonnhard Graubner
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2

Nope.

For any function $f$, $|f(x_0)|=f(x_0)$ if and only if $f(x_0)\ge 0$; $|f(x_0)|=-f(x_0)$ if $f(x_0)\lt 0$.

On your particular occasion, doing case work, one could easily find that:

When $-x+3\ge 0\Rightarrow x\le 3, |-x+3|=-x+3$; When $-x+3\lt 0\Rightarrow x\gt 3, |-x+3|=x-3$.

When $x+3\ge 0\Rightarrow x\ge -3, |x+3|=x+3$; When $x+3\lt 0\Rightarrow x\lt -3, |x+3|=-x-3$.

BAI
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