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

The solution to sqrt(3x+7)-sqrt(x-2)>3 is 2 6

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

3 x + 7 - x - 2 > 3

2 \leq x < 3 or x > 6

Interval Notation

[2, 3) \cup (6, \infty)

Solution steps

3 x + 7 - x - 2 > 3

Add

x - 2

to both sides

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

Simplify

3 x + 7 > 3 + x - 2

f (x) > g (x)

then

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

For

3 + x - 2 < 0 :

No Solution

For

3 + x - 2 \geq 0 : 0 < x < 3 or x > 6

Find singularity points

Find non-negative values for radicals:

x \geq 2

Combine the intervals

(0 < x < 3 or x > 6 or No Solution) and x \geq 2

Merge Overlapping Intervals

2 \leq x < 3 or x > 6

Verify Solutions:

2 \leq x < 3

True

, x > 6

True

The solution is

2 \leq x < 3 or x > 6

R = 5 \cdot 37414 - 3400 \cdot 59.2

2.5 E - 16 = \frac{x ^{2}}{0.76}

6 x - 13 x

n^{2} = 25

\frac{x}{2} - 6 = 12

What is sqrt(3x+7)-sqrt(x-2)>3 ?
The solution to sqrt(3x+7)-sqrt(x-2)>3 is 2<= x<3\lor x>6