What is x-3sqrt(x-1)+3>0 ?

The solution to x-3sqrt(x-1)+3>0 is x>= 1

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x-3sqrt(x-1)+3>0

x - 3 x - 1 + 3 > 0

x \geq 1

Interval Notation

[1, \infty)

Solution steps

x - 3 x - 1 + 3 > 0

Subtract

x + 3

from both sides

x - 3 x - 1 + 3 - (x + 3) > 0 - (x + 3)

Simplify

- 3 x - 1 > - (x + 3)

Multiply both sides by

- 1

3 x - 1 < x + 3

Divide both sides by

3

x - 1 < \frac{x + 3}{3}

f (x) < g (x)

then

g (x) > 0

\frac{x + 3}{3} > 0 : x > - 3

x - 1 < \frac{x + 3}{3} :

True for all

x

Find singularity points

Find non-negative values for radicals:

x \geq 1

Combine the intervals

x > - 3 and True for all x and x \geq 1

Merge Overlapping Intervals

x \geq 1

Verify Solutions:

x \geq 1

True

The solution is

x \geq 1

2 x^{4} + 7 x^{3} - 15 x^{2}

0 = n - 78

(a + b)^{2} - (a - b)^{2}

\frac{3}{4} (x - 5) = \frac{2}{3} (3 x - 4)

(3 a + 2)^{3} - 8 a^{3}