What is sqrt(x-1)>sqrt(3-x) ?

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

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sqrt(x-1)>sqrt(3-x)

x - 1 > 3 - x

2 < x \leq 3

Interval Notation

(2, 3]

Solution steps

x - 1 > 3 - x

Square both sides

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

Simplify

x - 1 > 3 - x

x - 1 > 3 - x : x > 2

x > 2

Find singularity points

Find non-negative values for radicals:

1 \leq x \leq 3

Combine the intervals

x > 2 and 1 \leq x \leq 3

Merge Overlapping Intervals

2 < x \leq 3

x^{2} - 4 x > x - 2

(x - 8)^{\frac{1}{2}} - (18 - x)^{\frac{1}{2}} > (2)^{\frac{1}{2}}

x - 2 + 2 \leq x

x - 3 < x - 2

x^{2} + 1 > x - 1