What is sqrt(2x-3)-sqrt(x-2)>2 ?

The solution to sqrt(2x-3)-sqrt(x-2)>2 is x>4sqrt(7)+13

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sqrt(2x-3)-sqrt(x-2)>2

2 x - 3 - x - 2 > 2

x > 47 + 13

Interval Notation

(47 + 13, \infty)

Decimal Notation

x > 23.58300 \dots

Solution steps

2 x - 3 - x - 2 > 2

Add

x - 2

to both sides

2 x - 3 - x - 2 + x - 2 > 2 + x - 2

Simplify

2 x - 3 > 2 + x - 2

f (x) > g (x)

then

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

For

2 + x - 2 < 0 :

No Solution

For

2 + x - 2 \geq 0 : x > 47 + 13

Find singularity points

Find non-negative values for radicals:

x \geq 2

Combine the intervals

(x > 47 + 13 or No Solution) and x \geq 2

Merge Overlapping Intervals

x > 47 + 13

Verify Solutions:

x > 47 + 13

True

The solution is

x > 47 + 13

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

2 x < x^{2}

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

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

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

What is sqrt(2x-3)-sqrt(x-2)>2 ?
The solution to sqrt(2x-3)-sqrt(x-2)>2 is x>4sqrt(7)+13