a. $|x+5|=100$
⇒ \(\left[ \begin{array}{l}x+5=100\\x+5=-100\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=100-5\\x=-100-5\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=95\\x=-105\end{array} \right.\)
b. $100-| 25-x | = 40$
⇒ $| 25-x | =100-40$
⇒ $| 25-x | =60$
⇒ \(\left[ \begin{array}{l}25-x=60\\25-x=-60\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=25-60\\x=25-(-60)\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=-35\\x=85\end{array} \right.\)
c. $|2x+1| = | 23-x |$
⇒ \(\left[ \begin{array}{l}2x+1=23-x\\2x+1=-(23-x)\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}2x+x=23-1\\2x+1=-23+x\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}3x=22\\2x-x=-23-1\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=\frac{22}{3}\\x=-24\end{array} \right.\)
d. $|11-7x| - | 4x + 3|=0$
⇒ $|11-7x| = | 4x + 3|$
⇒ \(\left[ \begin{array}{l}11-7x=4x+3\\11-7x=-(4x+3)\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}-7x-4x=3-11\\11-7x=-4x-3\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}-11x=-8\\4x-7x=-3-11\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=\frac{8}{11}\\-3x=-14\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x=\frac{8}{11}\\x=\frac{14}{3}\end{array} \right.\)
