What is sqrt(2x+1)+sqrt(x-1)<1 ?

The solution to sqrt(2x+1)+sqrt(x-1)<1 is No Solution for x\in\mathbb{R}

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sqrt(2x+1)+sqrt(x-1)<1

2 x + 1 + x - 1 < 1

No Solution for x \in R

Solution steps

2 x + 1 + x - 1 < 1

Subtract

x - 1

from both sides

2 x + 1 + x - 1 - x - 1 < 1 - x - 1

Simplify

2 x + 1 < 1 - x - 1

f (x) < g (x)

then

g (x) > 0

1 - x - 1 > 0 : x < 2

2 x + 1 < 1 - x - 1 : x < - 1

Find singularity points

Find non-negative values for radicals:

x \geq 1

Combine the intervals

x < 2 and x < - 1 and x \geq 1

Merge Overlapping Intervals

No Solution for x \in R

∣ - 1 ∣ - ∣ - 5 ∣

x^{2} - 100 < 0

5 x^{2} - 37 x + 14

What is sqrt(2x+1)+sqrt(x-1)<1 ?
The solution to sqrt(2x+1)+sqrt(x-1)<1 is No Solution for x\in\mathbb{R}