What is sqrt(2x)+3>= sqrt(3x)+4 ?

The solution to sqrt(2x)+3>= sqrt(3x)+4 is No Solution

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sqrt(2x)+3>= sqrt(3x)+4

2 x + 3 \geq 3 x + 4

No Solution

Solution steps

2 x + 3 \geq 3 x + 4

Move

3 x

to the left side

2 x + 3 - 3 x \geq 4

Move

3

to the right side

2 x + 3 - 3 x \geq 1

Subtract

3

from both sides

2 x + 3 - 3 x - 3 \geq 1 - 3

Simplify

2 x - 3 x \geq - 2

Apply radical rule:

assuming

a \geq 0, b \geq 0

2 x - 3 x \geq - 2

Move

3 x

to the right side

2 x \geq - 2 + 3 x

f (x) \geq g (x)

then

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

For

- 2 + 3 x < 0 : 0 \leq x < \frac{4}{3}

For

- 2 + 3 x \geq 0 : \frac{4}{3} \leq x \leq 86 + 20

Find singularity points

Find non-negative values for radicals:

x \geq 0

Combine the intervals

(\frac{4}{3} \leq x \leq 86 + 20 or 0 \leq x < \frac{4}{3}) and x \geq 0

Merge Overlapping Intervals

0 \leq x \leq 86 + 20

Verify Solutions:

0 \leq x \leq 86 + 20

False

The solution is

No Solution for x \in R

x - 8 \geq 12 - x

x < 12

\frac{1}{2 \cdot 5 x} < 10

5 - x^{2} > x - 1

\frac{- ( x + 6 )}{( x - 2 )} < 3

What is sqrt(2x)+3>= sqrt(3x)+4 ?
The solution to sqrt(2x)+3>= sqrt(3x)+4 is No Solution