What is sqrt(2x+14)>x+3 ?

The solution to sqrt(2x+14)>x+3 is -7<= x<1

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sqrt(2x+14)>x+3

2 x + 14 > x + 3

- 7 \leq x < 1

Interval Notation

[- 7, 1)

Solution steps

2 x + 14 > x + 3

f (x) > g (x)

then

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

For

x + 3 < 0 : x < - 3

For

x + 3 \geq 0 : - 3 \leq x < 1

Find singularity points

Find non-negative values for radicals:

x \geq - 7

Combine the intervals

(- 3 \leq x < 1 or x < - 3) and x \geq - 7

Merge Overlapping Intervals

- 7 \leq x < 1

Verify Solutions:

- 7 \leq x < 1

True

The solution is

- 7 \leq x < 1

\frac{( x - 3 )}{( x - 2 )} > 1

x > (2 - x)^{\frac{1}{2}}

x - 1 - 8 - 2 x \geq 1

\frac{2}{( 3 x - 5 )} \geq 0

3 - x > 3 (1 - x^{2})^{\frac{1}{2}}