What is sqrt(2x-8)+sqrt(x-5)>sqrt(3x-9) ?

The solution to sqrt(2x-8)+sqrt(x-5)>sqrt(3x-9) is x>6

Popular >

sqrt(2x-8)+sqrt(x-5)>sqrt(3x-9)

2 x - 8 + x - 5 > 3 x - 9

x > 6

Interval Notation

(6, \infty)

Solution steps

2 x - 8 + x - 5 > 3 x - 9

Subtract

x - 5

from both sides

2 x - 8 + x - 5 - x - 5 > 3 x - 9 - x - 5

Simplify

2 x - 8 > 3 x - 9 - x - 5

f (x) > g (x)

then

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

For

3 x - 9 - x - 5 < 0 :

No Solution

For

3 x - 9 - x - 5 \geq 0 : 2 \leq x < 3 or x > 6

Find singularity points

Find non-negative values for radicals:

x \geq 5

Combine the intervals

(2 \leq x < 3 or x > 6 or No Solution) and x \geq 5

Merge Overlapping Intervals

x > 6

Verify Solutions:

x > 6

True

The solution is

x > 6

\frac{( x - 3 ) ^{2}}{2} - x + x^{2} = x - (x - 2)

3 c + 10 = 28

3 q - 2 \leq - 10 or 3 q - 2 > 10

4 u^{2} v + 16 u v^{2} + 16 v^{3}

\frac{6 ^{5}}{6 ^{2}}

What is sqrt(2x-8)+sqrt(x-5)>sqrt(3x-9) ?
The solution to sqrt(2x-8)+sqrt(x-5)>sqrt(3x-9) is x>6