Absolute Value

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Absolute Value
  • Is the value for a real number, disregarding the sign. Written [math]\left|x\right|[/math].
  • Mathematically defined as:
[math]\left|x\right|=x\text { if }x\geqq 0[/math]

[math]\left|x\right|=-x\text { if }x\lt0[/math]
  • Geometrically, [math]\left|x\right|[/math] is the distance of [math]x \text { to } 0\,[/math], and from [math]-x \text { to } 0\,[/math].


[math]\left|+3\right| = 3[/math]

[math]\left|-45\right| = 45[/math]

[math]\left|0\right| = 0[/math]

[math]\left|+5\right| =\left|-5\right| = 5[/math]

Absolute value properties

[math]\text{1) if }\left|x\right| = a\qquad\text{then}\quad x=a \qquad\text{or}\quad x=-a[/math]

[math]\text{2) if }\left|x\right| \lt a\qquad\text{then}\quad -a\ltx\lta[/math]

[math]\text{3) if }\left|x\right| \gt a\qquad\text{then}\quad x\gta \qquad\text{or}\quad x\lt-a[/math]

[math]\text{4) }\left|x\right|^2 = x ^ 2[/math]

[math]\text{5) }\left|x\right| = sqr(x^2)[/math]