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

The solution to sqrt(5-x)>x+1 is x<1

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sqrt(5-x)>x+1

5 - x > x + 1

x < 1

Interval Notation

(- \infty, 1)

Solution steps

5 - x > x + 1

f (x) > g (x)

then

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

For

x + 1 < 0 : x < - 1

For

x + 1 \geq 0 : - 1 \leq x < 1

Find singularity points

Find non-negative values for radicals:

x \leq 5

Combine the intervals

(- 1 \leq x < 1 or x < - 1) and x \leq 5

Merge Overlapping Intervals

x < 1

Verify Solutions:

x < 1

True

The solution is

x < 1

(3 x - 4) (4 x - 3) - (2 x - 7) (3 x - 2) = 214

\frac{5}{3} \cdot 5

x \cdot (x + 4) = x^{2} + 8

m^{2} - m - 88 = 0

3 ∣ 3 x ∣ + 4 = 16