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\(\frac{31}{9}\left|x\right|-\frac{5}{2}=\frac{8}{3}\)
=> \(\frac{31}{9}\left|x\right|=\frac{8}{3}+\frac{5}{2}\)
=> \(\frac{31}{9}\left|x\right|=\frac{16}{6}+\frac{15}{6}\)
=> \(\frac{31}{9}\left|x\right|=\frac{31}{6}\)
=> \(\left|x\right|=\frac{31}{6}:\frac{31}{9}=\frac{31}{6}\cdot\frac{9}{31}=\frac{9}{6}=\frac{3}{2}\)
=> x = 3/2 hoặc x = -3/2
a, x + 1/9 - 3/5 = 3/6
x + 1/9 = 3/6 - 3/5
x + 1/9 = -1/10
x = -1/10 - 1/9
x = -19/90
Có: \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}...\frac{30}{62}.\frac{31}{64}=\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}...\frac{30}{2.31}.\frac{31}{2.32}=\frac{1}{2}.\frac{1}{2}.\frac{1}{2}...\frac{1}{2}.\frac{1}{2}.\frac{1}{32}\)
\(=\frac{1}{2^{31}.2^5}=\frac{1}{2^{36}}=2^x\)\(\Rightarrow1=2^x.2^{36}=2^{36+x}\)\(\Rightarrow2^{36+x}=2^0\Rightarrow36+x=0\Rightarrow x=-36\)
Đề:
Giài:
\(\frac{31}{9}\left|x\right|=\frac{8}{3}+\frac{5}{2}\)
\(\frac{31}{9}\left|x\right|=\frac{31}{6}\)
\(\left|x\right|=\frac{31}{6}:\frac{31}{9}\)
\(\left|x\right|=\frac{3}{2}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=\frac{-3}{2}\end{cases}}\)
Vậy x = \(\frac{3}{2}\)hoặc x = \(\frac{-3}{2}\)
\(\frac{31}{9}\left|x\right|-\frac{5}{2}=\frac{8}{3}\)
\(\frac{31}{9}\left|x\right|=\frac{8}{3}+\frac{5}{2}\)
\(\frac{31}{9}\left|x\right|=\frac{8\cdot2}{6}+\frac{5\cdot3}{6}\)
\(\frac{31}{9}\left|x\right|=\frac{16}{6}+\frac{15}{6}\)
\(\frac{31}{9}\left|x\right|=\frac{31}{6}\)
\(\left|x\right|=\frac{31}{6}:\frac{31}{9}\)
\(\left|x\right|=\frac{31}{6}\cdot\frac{9}{31}\)
\(\left|x\right|=\frac{1}{2}\cdot\frac{3}{1}\)
\(\Leftrightarrow\hept{\begin{cases}x=\frac{3}{2}\\x=-\frac{3}{2}\end{cases}}\)
Vậy \(x\in\left\{\frac{3}{2};-\frac{3}{2}\right\}\)