What is sqrt(x-1)<2 ?

The solution to sqrt(x-1)<2 is 1<= x<5

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sqrt(x-1)<2

x - 1 < 2

1 \leq x < 5

Interval Notation

Solution steps

x - 1 < 2

Square both sides

(x - 1)^{2} < 2^{2}

Simplify

x - 1 < 4

Move

1

to the right side

x < 5

Find singularity points

Find non-negative values for radicals:

x \geq 1

Combine the intervals

x < 5 and x \geq 1

Merge Overlapping Intervals

1 \leq x < 5

4 x^{2} + 15 = - 9

- 126 = 21 r

7 3 x - 3 \geq 21

∣ - 6 x - 6 ∣ = 3 x - 6

- \frac{3}{20} - \frac{2}{5} \cdot 0.5