Đáp án:
$|3x-4|=|5-x|$
$⇔ |3x-4|-|5-x|=0$
$TH1: $
\(\left[ \begin{array}{l}3x-4≥0\\5-x≥0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}x≥4/3\\x≤5\end{array} \right.\)
$⇔ 3x-4-(5-x)=0$
$⇔ 3x-4-5+x=0$
$⇔ 4x-9=0$
$⇔ 4x=9$
$⇔ x=9/4$ (nhận)
$TH2: $
\(\left[ \begin{array}{l}3x-4≤0\\5-x≤0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}x≤4/3\\x≥5\end{array} \right.\)
$⇔ 4-3x-(x-5)=0$
$⇔ 4-3x-x+5=0$
$⇔ -4x+9=0$
$⇔ -4x=-9$
$⇔ x=9/4 $(loại)
$TH3: $
\(\left[ \begin{array}{l}3x-4≥0\\5-x<0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}x≥4/3\\x>5\end{array} \right.\)
$⇔ 3x-4-(x-5)=0$
$⇔ 3x-4-x+5=0$
$⇔ 2x+1=0$
$⇔ 2x=-1$
$⇔ x=-0,5$ (loại)
$TH4: $
\(\left[ \begin{array}{l}3x-4<0\\5-x≥0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}x<4/3\\x<5\end{array} \right.\)
$⇔ 4-3x-(5-x)=0$
$⇔ 4-3x-5+x=0$
$⇔ -2x-1=0$
$⇔ -2x=1$
$⇔ x=-0,5$ (nhận)
Vậy $S=${$-0,5; 9/4$}
BẠN THAM KHẢO NHA!!!
