What is (2/5)^{((1-5x))/((4+16))}< 25/4 ?

The solution to (2/5)^{((1-5x))/((4+16))}< 25/4 is x< 41/5

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(2/5)^{((1-5x))/((4+16))}< 25/4

(\frac{2}{5})^{\frac{( 1 - 5 x )}{( 4 + 16 )}} < \frac{25}{4}

x < \frac{41}{5}

Interval Notation

(- \infty, \frac{41}{5})

Decimal Notation

x < 8.2

Solution steps

(\frac{2}{5})^{\frac{( 1 - 5 x )}{( 4 + 16 )}} < \frac{25}{4}

Apply exponent rules

\frac{1 - 5 x}{4 + 16} > - 2

Simplify

\frac{1 - 5 x}{20} > - 2

\frac{1 - 5 x}{20} > - 2 : x < \frac{41}{5}

x < \frac{41}{5}

4^{x - 1} + 2^{x + 1} \geq 2^{5}

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

e^{- 2 x^{2}} - 1 > 0

3^{x} \leq 4^{x}

9^{x} + 3^{x} - 6 > 0

What is (2/5)^{((1-5x))/((4+16))}< 25/4 ?
The solution to (2/5)^{((1-5x))/((4+16))}< 25/4 is x< 41/5