What is sqrt(2x-9)<= 3-x ?

The solution to sqrt(2x-9)<= 3-x is No Solution for x\in\mathbb{R}

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sqrt(2x-9)<= 3-x

2 x - 9 \leq 3 - x

No Solution for x \in R

Solution steps

2 x - 9 \leq 3 - x

f (x) \leq g (x)

then

g (x) \geq 0

3 - x \geq 0 : x \leq 3

2 x - 9 \leq 3 - x :

True for all

x

Find singularity points

Find non-negative values for radicals:

x \geq \frac{9}{2}

Combine the intervals

x \leq 3 and True for all x and x \geq \frac{9}{2}

Merge Overlapping Intervals

No Solution for x \in R

3 lo g_{2} (8) + 4 lo g_{2} (\frac{1}{2}) - lo g_{3} (2)

3 x^{2} - 8 x + 7 = 0

(8 x + 7)^{2} = 27

10 - (4 - x) = 20 + (x - 4)

(\frac{2 x ^{3} y ^{2} z}{3 x ^{4} y z ^{- 2}})^{- 2}

What is sqrt(2x-9)<= 3-x ?
The solution to sqrt(2x-9)<= 3-x is No Solution for x\in\mathbb{R}