What is sqrt(x)>7-x ?

The solution to sqrt(x)>7-x is x>(-sqrt(29)+15)/2

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sqrt(x)>7-x

x > 7 - x

x > \frac{- 29 + 15}{2}

Interval Notation

(\frac{- 29 + 15}{2}, \infty)

Decimal Notation

x > 4.80741 \dots

Solution steps

x > 7 - x

f (x) > g (x)

then

g (x) < 0 or g (x) \geq 0

For

7 - x < 0 : x > 7

For

7 - x \geq 0 : \frac{- 29 + 15}{2} < x \leq 7

Find singularity points

Find non-negative values for radicals:

x \geq 0

Combine the intervals

(\frac{- 29 + 15}{2} < x \leq 7 or x > 7) and x \geq 0

Merge Overlapping Intervals

x > \frac{- 29 + 15}{2}

Verify Solutions:

x > \frac{- 29 + 15}{2}

True

The solution is

x > \frac{- 29 + 15}{2}

x^{2} - 3 x - 88 = 0

((2^{4})^{5})^{6}

7^{2} + 6^{2} = x^{2}

3 - \frac{3}{4} x > 3

\frac{2 x - 1}{x + 2} \leq 4