What is sqrt(5-x)-sqrt(x+1)>1 ?

The solution to sqrt(5-x)-sqrt(x+1)>1 is -1<= x<-(sqrt(11))/2+2

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sqrt(5-x)-sqrt(x+1)>1

5 - x - x + 1 > 1

- 1 \leq x < - \frac{11}{2} + 2

Interval Notation

[- 1, - \frac{11}{2} + 2)

Decimal Notation

- 1 \leq x < 0.34168 \dots

Solution steps

5 - x - x + 1 > 1

Add

x + 1

to both sides

5 - x - x + 1 + x + 1 > 1 + x + 1

Simplify

5 - x > 1 + x + 1

f (x) > g (x)

then

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

For

1 + x + 1 < 0 :

No Solution

For

1 + x + 1 \geq 0 : x < - \frac{11}{2} + 2

Find singularity points

Find non-negative values for radicals:

- 1 \leq x \leq 5

Combine the intervals

(x < - \frac{11}{2} + 2 or No Solution) and - 1 \leq x \leq 5

Merge Overlapping Intervals

- 1 \leq x < - \frac{11}{2} + 2

Verify Solutions:

- 1 \leq x < - \frac{11}{2} + 2

True

The solution is

- 1 \leq x < - \frac{11}{2} + 2

- 32 t = 0

2 x \leq - 16

14 + m \leq 12

(x + 2)^{2} = 1 - x (x + 3)

\frac{( x + 2 ) ( x - 2 )}{4} - \frac{( x - 3 ) ^{2}}{3} = \frac{x ( 11 - x )}{6}

What is sqrt(5-x)-sqrt(x+1)>1 ?
The solution to sqrt(5-x)-sqrt(x+1)>1 is -1<= x<-(sqrt(11))/2+2