sqrt(x+2)<= x-10

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√x+2≤ x−10

Solution

x≥ 14

Interval Notation

[14, ∞ )

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√x+2≤ x−10

If √f(x)≤ g(x) then g(x)≥ 0

x−10≥ 0: x≥ 10

√x+2≤ x−10: x≤ 7 or x≥ 14

Find singularity points

Find non-negative values for radicals: x≥ −2

Combine the intervals

x≥ 10 and (x≤ 7 or x≥ 14) and x≥ −2

Merge Overlapping Intervals

x≥ 14

Verify Solutions: x≥ 14 True

The solution is

x≥ 14

Number Line

x≥ 14

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

sqrt(x+2)<= x-10

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