What is sqrt(2x+14)-6>= 4 ?

The solution to sqrt(2x+14)-6>= 4 is x>= 43

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sqrt(2x+14)-6>= 4

2 x + 14 - 6 \geq 4

x \geq 43

Interval Notation

[43, \infty)

Solution steps

2 x + 14 - 6 \geq 4

Move

6

to the right side

2 x + 14 \geq 10

Square both sides

(2 x + 14)^{2} \geq 1 0^{2}

Simplify

2 x + 14 \geq 100

2 x + 14 \geq 100 : x \geq 43

x \geq 43

Find singularity points

Find non-negative values for radicals:

x \geq - 7

Combine the intervals

x \geq 43 and x \geq - 7

Merge Overlapping Intervals

x \geq 43

7 x^{\frac{5}{2}}

2 x - 10 = - 32

3 \leq x < 7

3^{2} + 5^{2}