Cách giải:
$1,|5x-4|=2x+1$
$ĐK:x \geq \dfrac{-1}{2}$
$→\left[ \begin{array}{l}5x-4=2x+1\\5x-4=-2x-1\end{array} \right.$
$→\left[ \begin{array}{l}3x=5\\7x=3\end{array} \right.$
$→\left[ \begin{array}{l}x=\dfrac{5}{3}(TM)\\x=\dfrac{3}{7}(TM)\end{array} \right.$
Vậy $\left[ \begin{array}{l}x=\dfrac{5}{3}(TM)\\x=\dfrac{3}{7}(TM)\end{array} \right.$
$2,A=(-7)+(-7)^2+(-7)^3+....+(-7)^{51}$
$→A=-7+7^2-7^3+....-7^{51}$
$→7A=-7^2+7^3-7^4+......-7^{52}$
$→7A+A=8A=-7^{52}-7$
$→A=\dfrac{-7^{52}-7}{8}$
