by Tìm \(x\), biết
a. \(\frac{2}{3} + \frac{7}{4}:x = \frac{5}{6}\)
b. \(\frac{3}{2} – \left( {x – \frac{5}{6}} \right) = \frac{8}{9}\)
c. \(\left( {4x – 9} \right)\left( {2,5 + \frac{{ – 7}}{3}x} \right) = 0\)
A. a) \( x = \frac{{21}}{2} \)
b) \( x = \frac{{13}}{9} \)
c) \(x = \frac{9}{4}\) hoặc \(x = \frac{{15}}{{14}}\)
B. a) \( x = \frac{{21}}{2} \)
b) \( x = \frac{{13}}{9} \)
c) \(x = \frac{9}{4}\)
C. a) \( x = -\frac{{21}}{2} \)
b) \( x = 0 \)
c) \(x = \frac{9}{4}\) hoặc \(x = \frac{{15}}{{14}}\)
D. a) \( x = \frac{{21}}{2} \)
b) \( x = -\frac{{13}}{9} \)
c) \( x = \frac{{15}}{{14}}\)
Hướng dẫn
Chọn đáp án là: A
\(\begin{array}{l}a)\frac{2}{3} + \frac{7}{4}:x = \frac{5}{6}\\\frac{7}{4}:x = \frac{5}{6} – \frac{2}{3}\\\frac{7}{4}:x = \frac{5}{6} – \frac{4}{6}\\\frac{7}{4}:x = \frac{1}{6}\\x = \frac{7}{4}:\frac{1}{6}\\x = \frac{{21}}{2}\end{array}\)
\(\begin{array}{l}b)\frac{3}{2} – \left( {x – \frac{5}{6}} \right) = \frac{8}{9}\\x – \frac{5}{6} = \frac{3}{2} – \frac{8}{9}\\x – \frac{5}{6} = \frac{{27}}{{18}} – \frac{{16}}{{18}}\\x – \frac{5}{6} = \frac{{11}}{{18}}\\x = \frac{{11}}{{18}} + \frac{5}{6}\\x = \frac{{13}}{9}\end{array}\)
c) \(\left( {4x – 9} \right)\left( {2,5 + \frac{{ – 7}}{3}x} \right) = 0\)
\( \Rightarrow 4x – 9 = 0\) hoặc \(2,5 + \frac{{ – 7}}{3}x = 0\)
+) \(4x – 9 = 0 \Rightarrow x = \frac{9}{4}\)
+) \(2,5 + \frac{{ – 7}}{3}x = 0 \Rightarrow \frac{{ – 7}}{3}x = – 2,5\)
\(x = – 2,5:\frac{{ – 7}}{3}\)
\(x = \frac{{15}}{{14}}\)
Vậy \(x = \frac{9}{4}\) hoặc \(x = \frac{{15}}{{14}}\)
