What is sqrt(5-x)<3 ?

The solution to sqrt(5-x)<3 is -4<x<= 5

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sqrt(5-x)<3

5 - x < 3

- 4 < x \leq 5

Interval Notation

(- 4, 5]

Solution steps

5 - x < 3

Square both sides

(5 - x)^{2} < 3^{2}

Simplify

5 - x < 9

5 - x < 9 : x > - 4

x > - 4

Find singularity points

Find non-negative values for radicals:

x \leq 5

Combine the intervals

x > - 4 and x \leq 5

Merge Overlapping Intervals

- 4 < x \leq 5

x^{2} + x > 1 - 2 x

x - 1 < 7 - x

n - 3 \geq 3 n + 1

x + 6 < x - 6

(m + 2) + (4 m + 5)^{\frac{1}{2}} > 1