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

The solution to sqrt(x-1)>x-3 is 1<= x<5

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sqrt(x-1)>x-3

x - 1 > x - 3

1 \leq x < 5

Solution steps

x - 1 > x - 3

f (x) > g (x)

then

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

For

x - 3 < 0 : x < 3

For

x - 3 \geq 0 : 3 \leq x < 5

Find singularity points

Find non-negative values for radicals:

x \geq 1

Combine the intervals

(3 \leq x < 5 or x < 3) and x \geq 1

Merge Overlapping Intervals

1 \leq x < 5

Verify Solutions:

1 \leq x < 5

True

The solution is

1 \leq x < 5

- 25 + \frac{t}{2} \geq 50

- 3 (2 + 4 k) + 7 (2 k - 1)

e^{0.25}

6 x + 9 = x^{2}

- 2 x + 3 < 9