Tìm x , biết: e) trị tuyệt đối của ( x + 4/ 15 ) − | − 3 , 75 | = − | − 2 , 15 | ;
Giải thích
e) \(\left| {x + \frac{4}{{15}}} \right| - \left| { - 3,75} \right| = - \left| { - 2,15} \right|\)
\(\left| {x + \frac{4}{{15}}} \right| = - 2,15 + 3,75\)
\(\left| {x + \frac{4}{{15}}} \right| = 1,6\)
\(\left| {x + \frac{4}{{15}}} \right| = \frac{8}{5}\)
TH1: \[x + \frac{4}{{15}} = \frac{8}{5}\]
\[x = \frac{8}{5} - \frac{4}{{15}}\]
\[x = \frac{{24}}{{15}} - \frac{4}{{15}}\]
\[x = \frac{4}{3}\].
TH2: \[x + \frac{4}{{15}} = - \frac{8}{5}\]
\[x = - \frac{8}{5} - \frac{4}{{15}}\]
\[x = - \frac{{24}}{{15}} - \frac{4}{{15}}\]
\[x = - \frac{{28}}{{15}}\]
Vậy \[x \in \left\{ { - \frac{{28}}{{15}};\frac{4}{3}} \right\}\].