by \(\,\,1\frac{1}{4} – \left| {x + \frac{5}{6}} \right| = \frac{{ – 5}}{7}.\frac{{21}}{6}\)
A. \(x = \frac{{55}}{{12}}\) hoặc \(x = – \frac{{55}}{{12}}\).
B. \(x = \frac{{35}}{{12}}\) hoặc \(x = – \frac{{55}}{{12}}\).
C. \(x = \frac{{15}}{{12}}\) hoặc \(x = – \frac{{15}}{{12}}\).
D. \(x = \frac{{25}}{{12}}\) hoặc \(x = – \frac{{35}}{{12}}\).
Hướng dẫn
Chọn đáp án là: B
Phương pháp giải:
Sử dụng kiến thức: \(\left| A \right| = B > 0\) thì \(A = B\) hoặc \(A = – B\).
\(\,\,1\frac{1}{4} – \left| {x + \frac{5}{6}} \right| = \frac{{ – 5}}{7}.\frac{{21}}{6}\)
\(\begin{array}{l}\frac{5}{4} – \left| {x + \frac{5}{6}} \right| = – \frac{5}{2}\\\left| {x + \frac{5}{6}} \right| = \frac{5}{4} + \frac{5}{2}\\\left| {x + \frac{5}{6}} \right| = \frac{{15}}{4}\end{array}\)
+) TH1: \(x + \frac{5}{6} = \frac{{15}}{4}\)
\(\begin{array}{l}x = \frac{{15}}{4} – \frac{5}{6}\\x = \frac{{35}}{{12}}\end{array}\)
+) TH2: \(x + \frac{5}{6} = – \frac{{15}}{4}\)
\(\begin{array}{l}x = – \frac{{15}}{4} – \frac{5}{6}\\x = – \frac{{55}}{{12}}\end{array}\)
Vậy \(x = \frac{{35}}{{12}}\) hoặc \(x = – \frac{{55}}{{12}}\).
Chọn B
