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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

Solutions > Absolute Value Inequalities Calculator >

|a-8|>= 3

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

π

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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|a−8|≥ 3

Solution

a≤ 5 or a≥ 11

Interval Notation

(−∞ , 5]∪ [11, ∞ )

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Solution steps

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|a−8|≥ 3

Apply absolute rule: If |u| ≥ a, a > 0 then u ≤ −a or u ≥ a

a−8≤ −3 or a−8≥ 3

a−8≤ −3 or a−8≥ 3

a≤ 5 or a≥ 11

Number Line

a≤ 5 or a≥ 11

Absolute Value Inequalities Examples

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