a/ $15-x=1-(-9)$
$↔15-x=1+9=10$
$↔x=15-10=5$
b/ $-2x-3(x-17)=34-2(-x+25)$
$↔-2x-3x+51=34+2x-50$
$↔-5x+51=2x-16$
$↔-5x-2x=-16-51$
$↔-7x=-67$
$↔x=\dfrac{67}{7}$
c/ $2|x-3|-4=10$
$↔2|x-3|=14$
$↔|x-3|=7$
\(\leftrightarrow\left[ \begin{array}{l}x-3=7\\x-3=-7\end{array} \right.\)
\(\leftrightarrow\left[ \begin{array}{l}x=10\\x=-4\end{array} \right.\)
d/ $(x-3)(x+5)=17$
$→(x-3);(x+5)\in Ư(17)=\{±1;±17\}$
\(\to\left[ \begin{array}{l}\begin{cases}x-3=1\\x+5=17\end{cases}\\\begin{cases}x-3=17\\x+5=1\end{cases}\\\begin{cases}x-3=-1\\x+5=-17\end{cases}\\\begin{cases}x-3=-17\\x+5=-1\end{cases}\end{array} \right.\) \(\to\left[ \begin{array}{l}\begin{cases}x=4\\x=12\end{cases}(ktm)\\\begin{cases}x=20\\x=-4\end{cases}(ktm)\\\begin{cases}x=2\\x=-22\end{cases}(ktm)\\\begin{cases}x=-14\\x=-6\end{cases}(ktm)\end{array} \right.\)
$→x\in\{\varnothing\}$
