What is sqrt(2x-6)-2<0 ?

The solution to sqrt(2x-6)-2<0 is 3<= x<5

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sqrt(2x-6)-2<0

2 x - 6 - 2 < 0

3 \leq x < 5

Interval Notation

[3, 5)

Solution steps

2 x - 6 - 2 < 0

Move

2

to the right side

2 x - 6 < 2

Square both sides

(2 x - 6)^{2} < 2^{2}

Simplify

2 x - 6 < 4

2 x - 6 < 4 : x < 5

x < 5

Find singularity points

Find non-negative values for radicals:

x \geq 3

Combine the intervals

x < 5 and x \geq 3

Merge Overlapping Intervals

3 \leq x < 5

\frac{x}{4} = 16

(2 x - 2)^{2} + 1 = 6 - (x - 1)^{2}

x^{2} > 6 x - 9

4 a - 7 < 2 a + 1

y^{2} - 13 y + 22