Question

Rezolvati : a)5supra22 in paranteza rotunda,la puterea4x-5 ≤ decat 4,4.
b)0,2in paranteza rotunda la puterea a 3a≥125 la puterea x-4.

Answer 1

a) $( \frac{5}{22}) ^{4} *x-5 \leq 4.4$
$\frac{ 5^{4} }{ 22^{4} }*x-5 \leq \frac{22}{5}$
$\frac{ 5^{4}x }{ 22^{4} }-5 \leq \frac{22}{5}$
$\frac{ 625x }{ 22^{4} }-5 \leq \frac{22}{5}$
$5* 22^{4}* \frac{625x}{ 22^{4} }-5* 22^{4}*5 \leq 5*22^{4}* \frac{22}{5}$
$5*625x-25*22^{4} \leq22^{4}*22$
$3125x-25*22^{4} \leq 22^{5}$
$3125x \leq 22^{5}+25*22^{4}$
$3125x \leq (22+25)*22^{4}$
$3125x \leq 47*22^{4}$
$3125x:3125 \leq 47*22^{4}:3125$
$x \leq \frac{47*22^{4}}{3125}$ ≈ x≤3523.21024

b) ?