What is x-5>sqrt(4x+8)-4 ?

The solution to x-5>sqrt(4x+8)-4 is x>7

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x-5>sqrt(4x+8)-4

x - 5 > 4 x + 8 - 4

x > 7

Interval Notation

(7, \infty)

Solution steps

x - 5 > 4 x + 8 - 4

Switch sides

4 x + 8 - 4 < x - 5

Add

4

to both sides

4 x + 8 - 4 + 4 < x - 5 + 4

Simplify

4 x + 8 < x - 1

f (x) < g (x)

then

g (x) > 0

x - 1 > 0 : x > 1

4 x + 8 < x - 1 : x < - 1 or x > 7

Find singularity points

Find non-negative values for radicals:

x \geq - 2

Combine the intervals

x > 1 and (x < - 1 or x > 7) and x \geq - 2

Merge Overlapping Intervals

x > 7

Verify Solutions:

x > 7

True

The solution is

x > 7

2 (f + 3) - 2 = 8 + 2 f

\frac{9}{5} = \frac{z}{20}

x (x - 5) (x + 2) \leq 0

\frac{a ^{4} b ^{- 3}}{a b ^{- 2}}

16 x^{2} - 24 x y + 9 y^{2}