What is sqrt(x-1)>3-x ?

The solution to sqrt(x-1)>3-x is x>2

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sqrt(x-1)>3-x

x - 1 > 3 - x

x > 2

Interval Notation

(2, \infty)

Solution steps

x - 1 > 3 - x

f (x) > g (x)

then

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

For

3 - x < 0 : x > 3

For

3 - x \geq 0 : 2 < x \leq 3

Find singularity points

Find non-negative values for radicals:

x \geq 1

Combine the intervals

(2 < x \leq 3 or x > 3) and x \geq 1

Merge Overlapping Intervals

x > 2

Verify Solutions:

x > 2

True

The solution is

x > 2

x^{2} - 5 x + 4 \leq 2 x - 2

2 x - 3 - x - 2 > 2

(x - 8)^{\frac{1}{2}} \geq 12 - x

2 x < x^{2}

582 x^{2} - 9 x^{2}, 5 - 3 x + y + 6