What is sqrt(5-2x)<6x-1 ?

The solution to sqrt(5-2x)<6x-1 is 1/2 <x<= 5/2

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sqrt(5-2x)<6x-1

5 - 2 x < 6 x - 1

\frac{1}{2} < x \leq \frac{5}{2}

Interval Notation

(\frac{1}{2}, \frac{5}{2}]

Decimal Notation

0.5 < x \leq 2.5

Solution steps

5 - 2 x < 6 x - 1

f (x) < g (x)

then

g (x) > 0

6 x - 1 > 0 : x > \frac{1}{6}

5 - 2 x < 6 x - 1 : x < - \frac{2}{9} or x > \frac{1}{2}

Find singularity points

Find non-negative values for radicals:

x \leq \frac{5}{2}

Combine the intervals

x > \frac{1}{6} and (x < - \frac{2}{9} or x > \frac{1}{2}) and x \leq \frac{5}{2}

Merge Overlapping Intervals

\frac{1}{2} < x \leq \frac{5}{2}

Verify Solutions:

\frac{1}{2} < x \leq \frac{5}{2}

True

The solution is

\frac{1}{2} < x \leq \frac{5}{2}

6 x - x^{2} < 3 + x

\frac{- 3}{( x ^{2} + 2 x + 10 )} \geq 0

\frac{( x + 5 )}{∣ 1 - x ∣} > 1

5 - x < 3

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