Question

Resolva as inequações .

d) 4 x⁺¹ . 2 x⁻¹<128

Answer 1

$4^{x+1} . 2^{x-1} \ \textless \ 128 \\ \\ (2^2) ^{x+1} . 2^{x-1} \ \textless \ 2^7 \\ \\ 2^{2(x+1)} . 2^{x-1} \ \textless \ 2^7 \\ \\ 2^{2(x+1)+(x-1)} \ \textless \ 2^7 \\ \\ 2(x+1)+(x-1)\ \textless \ 7 \\ \\ 2x+2+x-1\ \textless \ 7 \\ \\ 3x+1\ \textless \ 7 \\ \\ 3x\ \textless \ 7-1 \\ \\ x\ \textless \ \frac{6}{3}$

                                     $x\ \textless \ 2$