What is sqrt(x+3)>sqrt(4-x) ?

The solution to sqrt(x+3)>sqrt(4-x) is 1/2 <x<= 4

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sqrt(x+3)>sqrt(4-x)

x + 3 > 4 - x

\frac{1}{2} < x \leq 4

Interval Notation

(\frac{1}{2}, 4]

Decimal Notation

0.5 < x \leq 4

Solution steps

x + 3 > 4 - x

Square both sides

(x + 3)^{2} > (4 - x)^{2}

Simplify

x + 3 > 4 - x

x + 3 > 4 - x : x > \frac{1}{2}

x > \frac{1}{2}

Find singularity points

Find non-negative values for radicals:

- 3 \leq x \leq 4

Combine the intervals

x > \frac{1}{2} and - 3 \leq x \leq 4

Merge Overlapping Intervals

\frac{1}{2} < x \leq 4

- (4 w^{- 3} z^{- 5}) (8 w)^{2}

- \frac{1}{6} - \frac{1}{6}

4 x < 24

x - 24 = 13

\frac{1}{3} + \frac{2}{4}