What is sqrt(3x+7)-sqrt(x-2)>9 ?

The solution to sqrt(3x+7)-sqrt(x-2)>9 is x>(9sqrt(217)+153)/2

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sqrt(3x+7)-sqrt(x-2)>9

3 x + 7 - x - 2 > 9

x > \frac{9 217 + 153}{2}

Interval Notation

(\frac{9 217 + 153}{2}, \infty)

Decimal Notation

x > 142.78913 \dots

Solution steps

3 x + 7 - x - 2 > 9

Add

x - 2

to both sides

3 x + 7 - x - 2 + x - 2 > 9 + x - 2

Simplify

3 x + 7 > 9 + x - 2

f (x) > g (x)

then

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

For

9 + x - 2 < 0 :

No Solution

For

9 + x - 2 \geq 0 : x > \frac{9 217 + 153}{2}

Find singularity points

Find non-negative values for radicals:

x \geq 2

Combine the intervals

(x > \frac{9 217 + 153}{2} or No Solution) and x \geq 2

Merge Overlapping Intervals

x > \frac{9 217 + 153}{2}

Verify Solutions:

x > \frac{9 217 + 153}{2}

True

The solution is

x > \frac{9 217 + 153}{2}

4 x + 5 \leq 5

(x - 2)^{4} + 10 (x - 2)^{2} + 9

2 x^{2} + 6 x + 18

5 x^{2} + 3 x + 9 = - 10 x + 3

h^{2} = 9

What is sqrt(3x+7)-sqrt(x-2)>9 ?
The solution to sqrt(3x+7)-sqrt(x-2)>9 is x>(9sqrt(217)+153)/2