What is sqrt(x+6)<x-6 ?

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sqrt(x+6)<x-6

x + 6 < x - 6

x > 10

Interval Notation

(10, \infty)

Solution steps

x + 6 < x - 6

f (x) < g (x)

then

g (x) > 0

x - 6 > 0 : x > 6

x + 6 < x - 6 : x < 3 or x > 10

Find singularity points

Find non-negative values for radicals:

x \geq - 6

Combine the intervals

x > 6 and (x < 3 or x > 10) and x \geq - 6

Merge Overlapping Intervals

x > 10

Verify Solutions:

x > 10

True

The solution is

x > 10

(m + 2) + (4 m + 5)^{\frac{1}{2}} > 1

x + 3 < x + 33

x < 2

\frac{x}{2} > 4

x < 2 - x