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a) \(\frac{x}{2}+\frac{2x}{3}+\frac{\left(x+1\right)}{4}+\frac{\left(2x+1\right)}{6}=\frac83\)
\(\frac{6x}{12}+\frac{4.2x}{12}+\frac{3\left(x+1\right)}{12}+\frac{2\left(2x+1\right)}{12}=\frac{4.8}{12}\)
\(6x+8x+3x+3+4x+2=32\)
\(21x+5=32\)
\(21x=27\)
\(x=\frac{27}{21}=\frac97\)
b) sửa đề: \(\frac{6}{6x-3}\Rightarrow\frac{6}{6x+3}\)
\(\frac{3}{2x+1}+\frac{10}{4x+2}-\frac{6}{6x+3}=\frac{12}{26}\)
\(\frac{3}{2x+1}+\frac{10}{2\left(2x+1\right)}-\frac{6}{3\left(2x+1\right)}=\frac{12}{26}\)
\(\frac{3}{2x+1}+\frac{5}{2x+1}-\frac{2}{2x+1}=\frac{6}{13}\)
\(\frac{6}{2x+1}=\frac{6}{13}\)
2x+1=13
2x=12
x=6
a) \(-\frac{3}{4}x+\frac{1}{6}x=1-2\frac{5}{9}\)
\(\left(-\frac{3}{4}+\frac{1}{6}\right).x=1-\frac{23}{9}\)
\(-\frac{7}{12}.x=-\frac{14}{9}\)
\(x=-\frac{14}{9}:\left(-\frac{7}{12}\right)\)
\(x=\frac{8}{3}\)
Vậy x = ...
b) \(\left|2x-\frac{3}{8}\right|+2\frac{3}{4}=3\frac{1}{16}\)
\(\left|2x-\frac{3}{8}\right|+\frac{11}{4}=\frac{49}{16}\)
\(\left|2x-\frac{3}{8}\right|=\frac{49}{16}-\frac{11}{4}\)
\(\left|2x-\frac{3}{8}\right|=\frac{5}{16}\)
\(\Rightarrow\left|2x-\frac{3}{8}\right|\in\text{{}\frac{5}{16};-\frac{5}{16}\)}
Nếu, \(2x-\frac{3}{8}=\frac{5}{16}\)
\(2x=\frac{11}{16}\)
\(x=\frac{11}{32}\)
Nếu, \(2x-\frac{3}{8}=-\frac{5}{16}\)
\(2x=\frac{1}{16}\)
\(x=\frac{1}{32}\)
Vậy \(x\in\text{{}\frac{1}{32};\frac{11}{32}\)}
1,\(\left(\frac{7}{2}-2x\right).\frac{4}{3}=\frac{22}{3}\)
\(x.\left(\frac{7}{2}-2\right)=\frac{22}{3}:\frac{4}{3}=\frac{22}{3}.\frac{3}{4}=\frac{11}{2}\)
\(x.\frac{3}{2}=\frac{11}{2}\)
\(x=\frac{11}{2}:\frac{3}{2}=\frac{11}{2}.\frac{2}{3}=\frac{11}{3}\)
a) \(x+\frac{1}{6}=-\frac{3}{8}\)
\(x=-\frac{3}{8}-\frac{1}{6}\)
\(x=-\frac{13}{24}\)
~ Thiên mã ~
b) \(\frac{1}{2}.x+\frac{1}{8}.x=\frac{3}{4}\)
\(x.\left(\frac{1}{2}+\frac{1}{8}\right)=\frac{3}{4}\)
\(\frac{5}{8}.x=\frac{3}{4}\)
\(x=\frac{6}{5}\)
~ Thiên Mã ~
a) \(\left(2x+\frac{1}{3}\right)^4\ge0\Rightarrow A\ge-1\)
Dấu \(=\)xảy ra khi \(2x+\frac{1}{3}=0\Leftrightarrow x=-\frac{1}{6}\).
b) \(\left(\frac{4}{9}x-\frac{2}{15}\right)^6\ge0\Rightarrow B\le3\)
Dấu \(=\)xảy ra khi \(\frac{4}{9}x-\frac{2}{15}=0\Leftrightarrow x=\frac{3}{10}\).
\(\Leftrightarrow-\frac{6x}{12}+\frac{4.2x}{12}+\frac{3\left(x+1\right)}{12}+\frac{2\left(2x+1\right)}{12}=\frac{4.8}{12}\)
\(-6x+8x+3\left(x+1\right)+2\left(2x+1\right)=32\)
\(-6x+8x+3x+3+4x+2=32\)
\(9x+5=32\)
\(9x=27\)
x=3
a) \(\frac{5}{6}=\frac{x-1}{x}\)
\(5x=6x-6\)
\(6x-5x=6\)
\(x=6\)
các câu còn lại lm tương tự
hok tốt!!
b) \(\frac{1}{2}=\frac{x+1}{3x}\)
\(\Rightarrow1.3x=2.\left(x+1\right)\)
\(3x=2x+2\)
\(3x-2x=2\)
\(x=2\)
Vậy x=2
các câu khác bạn làm tương tự
a. \(\frac{3}{5}+x=\frac{5}{6}\)
=> \(x=\frac{5}{6}-\frac{3}{5}\)
=> \(x=\frac{7}{30}\)
b. \(\left(3\frac{1}{2}+2x\right).\frac{8}{3}=\frac{16}{3}\)
=> \(3\frac{1}{2}+2x=\frac{16}{3}:\frac{8}{3}=2\)
=> \(2x=2-3\frac{1}{2}=2-\frac{7}{2}=-\frac{3}{2}\)
=> \(x=-\frac{3}{2}:2\)
=> \(x=-\frac{3}{4}\)
a) ta có: \(\frac{x-3}{6}=\frac{3}{2x-6}\)
\(\Rightarrow\left(x-3\right).\left(2x-6\right)=6.3\)
\(\Rightarrow x.\left(2x-6\right)-3.\left(2x-6\right)=18\)
\(2x^2-6x-6x+18=18\)
\(2x^2-12x+18=18\)
\(2x^2-12x=0\)
\(2x.\left(x-6\right)=0\)
\(\Rightarrow2x=0\Rightarrow x=0\)
\(x-6=0\Rightarrow x=6\)
KL: x =0 hoặc x = 6
b) ta có: \(\frac{x+6}{x+2}=\frac{2x+3}{2x-1}\)
\(\Rightarrow\left(x+6\right).\left(2x-1\right)=\left(x+2\right).\left(2x+3\right)\)
\(\Rightarrow x.\left(2x-1\right)+6.\left(2x-1\right)=x.\left(2x+3\right)+2.\left(2x+3\right)\)
\(2x^2-x+12x-6=2x^2+3x+4x+6\)
\(2x^2+11x-6=2x^2+7x+6\)
\(\Rightarrow2x^2+11x-2x^2-7x=6+6\)
\(3x=12\)
\(x=12:3\)
\(x=4\)
\(\frac{x-3}{6}=\frac{3}{2x-6}\Leftrightarrow\left(x-3\right).\left(2x-6\right)=18\Leftrightarrow2x^2-12x+18=18\Leftrightarrow2x^2-12x=0\)
\(\Leftrightarrow x^2-6x=0\Leftrightarrow x.\left(x-6\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x=6\end{cases}}\)
\(\frac{x+6}{x+2}=\frac{2x+3}{2x-1}\Leftrightarrow\left(x+6\right).\left(2x-1\right)=\left(2x+3\right).\left(x+2\right)\)
\(\Leftrightarrow2x^2+11x-6=2x^2+7x+6\Leftrightarrow4x-12=0\Leftrightarrow x=3\)
\(\frac{-x}{2}+\frac{2x}{3}+\frac{x+1}{4}+\frac{2x+1}{6}=\frac{8}{3}\)
\(\frac{2.-x}{4}+\frac{4x}{6}+\frac{x+1}{4}+\frac{2x+1}{6}=\frac{8}{3}\)
\(\frac{-2x}{4}+\frac{4x}{6}+\frac{x+1}{4}+\frac{2x+1}{6}=\frac{8}{3}\)
\(\frac{-2x+x+1}{4}+\frac{4x+2x+1}{6}=\frac{8}{3}\)
\(\frac{-1x+1}{4}+\frac{6x+1}{6}=\frac{8}{3}\)
\(\frac{3\left(-1x+1\right)}{3.4}+\frac{2\left(6x+1\right)}{2.6}=\frac{4.8}{4.3}\)
\(\frac{-3x+3}{12}+\frac{12x+2}{12}=\frac{24}{12}\)
\(\frac{-3x+3+12x+2}{12}=\frac{24}{12}\)
\(\frac{9x+5}{12}=\frac{24}{12}\)
=> 9x+5=24
=> 9x= 24-5
9x= 19
x= 19:9
x= \(\frac{19}{9}\)
vậy x= \(\frac{19}{9}\)