Mình trình bày đáp án trong hình nhé. 

 

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!!!