|x+5|-|x-3|=7,0000000000

Đáp án:

\(x = \frac{5}{2}.\)

Giải thích các bước giải: \(\begin{array}{l} \left| {x + 5} \right| - \left| {x - 3} \right| = 7\,\,\,\left( * \right)\\ + )\,\,\,Voi\,\,\,x < - 5 \Rightarrow \left\{ \begin{array}{l} \left| {x + 5} \right| = - x - 5\\ \left| {x - 3} \right| = - x + 3 \end{array} \right.\\ \Rightarrow \left( * \right) \Leftrightarrow - x - 5 + x - 3 = 7\\ \Leftrightarrow - 8 = 7\,\,\,\left( {vo\,\,ly} \right)\\ \Rightarrow pt\,\,VN.\\ + )\,\,\,Voi\,\, - 5 \le x < 3 \Rightarrow \left\{ \begin{array}{l} \left| {x + 5} \right| = x + 5\\ \left| {x - 3} \right| = - x + 3 \end{array} \right.\\ \Rightarrow \left( * \right) \Leftrightarrow x + 5 + x - 3 = 7\\ \Leftrightarrow 2x = 5 \Leftrightarrow x = \frac{5}{2}\,\,\,\left( {tm} \right)\\ + )\,\,Voi\,\,\,x \ge 3 \Rightarrow \left\{ \begin{array}{l} \left| {x + 5} \right| = x + 5\\ \left| {x - 3} \right| = x - 3 \end{array} \right.\\ \Rightarrow \left( * \right) \Leftrightarrow x + 5 - x + 3 = 7\\ \Leftrightarrow 0x = - 1\,\,\\ \Rightarrow pt\,\,VN.\\ Vay\,\,x = \frac{5}{2}. \end{array}\)