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

The solution to sqrt(4x-4)-2<4 is 1<= x<10

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sqrt(4x-4)-2<4

4 x - 4 - 2 < 4

1 \leq x < 10

Interval Notation

[1, 10)

Solution steps

4 x - 4 - 2 < 4

Move

2

to the right side

4 x - 4 < 6

Square both sides

(4 x - 4)^{2} < 6^{2}

Simplify

4 x - 4 < 36

4 x - 4 < 36 : x < 10

x < 10

Find singularity points

Find non-negative values for radicals:

x \geq 1

Combine the intervals

x < 10 and x \geq 1

Merge Overlapping Intervals

1 \leq x < 10

5 x^{2} - 2 x + 4 = 0

∣ 2 x - 9 ∣ - 4 > 3

\frac{5}{8} + \frac{1}{8}

3 x > - 9

2 x + 18 = 0