a) $|2x+1|-19=-7$
$|2x+1|=(-7)+19$
$|2x+1|=12$
\(\left[ \begin{array}{l}2x+1=12\\2x+1=-12\end{array} \right.\) ⇒ \(\left[ \begin{array}{l}2x=13\\2x=-11\end{array} \right.\) ⇒ \(\left[ \begin{array}{l}x=\frac{13}{2}\\x=\frac{-11}{2}\end{array} \right.\)
b) $-28-7.|-3x+15|=-70$
$7.|-3x+15|=(-28)-(-70)$
$7.|-3x+15|=42$
$|-3x+15|=42:7$
$|-3x+15|=6$
\(\left[ \begin{array}{l}-3x+15=6\\-3x+15=-6\end{array} \right.\) ⇒ \(\left[ \begin{array}{l}-3x=6-15\\-3x=(-6)-15\end{array} \right.\) ⇒ \(\left[ \begin{array}{l}-3x=-9\\-3x=-21\end{array} \right.\) ⇒ \(\left[ \begin{array}{l}x=(-9):(-3)\\x=(-21):(-3)\end{array} \right.\) ⇒ \(\left[ \begin{array}{l}x=3\\x=7\end{array} \right.\)
c) $|18-2|.|-x+5|=12$
$|-16x+80|=12$
\(\left[ \begin{array}{l}-16x+80=12\\-16x+80=-12\end{array} \right.\) ⇒ \(\left[ \begin{array}{l}-16x=12-80\\-16x=(-12)-80\end{array} \right.\) ⇒ \(\left[ \begin{array}{l}-16x=-68\\-16x=-92\end{array} \right.\) ⇒ \(\left[ \begin{array}{l}x=\frac{23}{4}\\x=\frac{17}{4}\end{array} \right.\)
d) $12-2.(-x+3)^{2}=-38$
$2.(-x+3)^{2}=12-(-38)$
$2.(-x+3)^{2}=50$
$(-x+3)^{2}=50:2$
$(-x+3)^{2}=25$
$(-x+3)=\sqrt{25}$
$(-x+3)=5$ \(\left[ \begin{array}{l}-x+3=5\\x-3=5\end{array} \right.\) ⇒ \(\left[ \begin{array}{l}-x=5-3\\x=5+3\end{array} \right.\) ⇒ \(\left[ \begin{array}{l}-x=2⇒x=-2\\x=8\end{array} \right.\)
e) $-20+3.(2x+1)^{3}=-101$
$3.(2x+1)^{3}=(-101)-(-20)$
$3.(2x+1)^{3}=-81$
$(2x+1)^{3}=(-81):3$
$(2x+1)^{3}=-27$
$(2x+1)^{3}=(-3)^{3}$
$2x+1=-3$
$2x=(-3)-1$
$2x=-4$
$x=(-4):2$
$x=-2$
