What is sqrt(x-2)<x-4 ?

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(x-2)<x-4

x - 2 < x - 4

x > 6

Interval Notation

(6, \infty)

Solution steps

x - 2 < x - 4

f (x) < g (x)

then

g (x) > 0

x - 4 > 0 : x > 4

x - 2 < x - 4 : x < 3 or x > 6

Find singularity points

Find non-negative values for radicals:

x \geq 2

Combine the intervals

x > 4 and (x < 3 or x > 6) and x \geq 2

Merge Overlapping Intervals

x > 6

Verify Solutions:

x > 6

True

The solution is

x > 6

x^{2} - 3 x + 2 > 2 x - 5

x - 4 < 2

(x^{2} - 1) \cdot x^{2} - x - 2 \geq 0

\frac{( 1 - 21 - 4 x - x ^{2} )}{( x + 1 )} \geq 0

x - 1 - ∣ x ∣ \leq 0