What is x>sqrt(1-x) ?

The solution to x>sqrt(1-x) is (sqrt(5)-1)/2 <x<= 1

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x>sqrt(1-x)

x > 1 - x

\frac{5 - 1}{2} < x \leq 1

Interval Notation

(\frac{5 - 1}{2}, 1]

Decimal Notation

0.61803 \dots < x \leq 1

Solution steps

x > 1 - x

Switch sides

1 - x < x

f (x) < g (x)

then

g (x) > 0

x > 0

1 - x < x : x < \frac{- 5 - 1}{2} or x > \frac{5 - 1}{2}

Find singularity points

Find non-negative values for radicals:

x \leq 1

Combine the intervals

x > 0 and (x < \frac{- 5 - 1}{2} or x > \frac{5 - 1}{2}) and x \leq 1

Merge Overlapping Intervals

\frac{5 - 1}{2} < x \leq 1

Verify Solutions:

\frac{5 - 1}{2} < x \leq 1

True

The solution is

\frac{5 - 1}{2} < x \leq 1

x + 5 < x + 7

x^{2} - 6 x + 8 \leq x + 1

\frac{( x - 1 )}{( x - 2 )} < 0

\frac{( x ^{2} - 13 x + 40 )}{( 19 x - x ^{2} - 78 )} \leq 0

x - 2 \geq - 1