a: \(x-\dfrac{1}{15}=\dfrac{1}{10}\)
=>\(x=\dfrac{1}{10}+\dfrac{1}{15}=\dfrac{3}{30}+\dfrac{2}{30}=\dfrac{5}{30}=\dfrac{1}{6}\)
b: \(-\dfrac{2}{15}-x=-\dfrac{3}{10}\)
=>\(x=-\dfrac{2}{15}-\dfrac{-3}{10}=-\dfrac{2}{15}+\dfrac{3}{10}=-\dfrac{4}{30}+\dfrac{9}{30}=\dfrac{5}{30}=\dfrac{1}{6}\)
c: \(x+\dfrac{1}{3}=\dfrac{2}{5}-\left(-\dfrac{1}{3}\right)\)
=>\(x+\dfrac{1}{3}=\dfrac{2}{5}+\dfrac{1}{3}\)
=>\(x=\dfrac{2}{5}\)
d: \(\dfrac{3}{7}-x=\dfrac{1}{4}-\dfrac{3}{5}\)
=>\(\dfrac{3}{7}-x=\dfrac{5}{20}-\dfrac{12}{20}=-\dfrac{7}{20}\)
=>\(x=\dfrac{3}{7}+\dfrac{7}{20}=\dfrac{60}{140}+\dfrac{49}{140}=\dfrac{109}{140}\)
e: \(\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\)
=>\(\left|x+\dfrac{4}{15}\right|=-2,15+3,75=1,6=\dfrac{8}{5}\)
=>\(\left[{}\begin{matrix}x+\dfrac{4}{15}=\dfrac{8}{5}=\dfrac{24}{15}\\x+\dfrac{4}{15}=-\dfrac{24}{15}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{20}{15}=\dfrac{4}{3}\\x=-\dfrac{28}{15}\end{matrix}\right.\)
f: \(x-\dfrac{3}{4}< \dfrac{2}{3}\)
=>\(x< \dfrac{2}{3}+\dfrac{3}{4}=\dfrac{8}{12}+\dfrac{9}{12}=\dfrac{17}{12}\)
`x-1/15 = 1/10`
`=> x = 1/5 + 1/15`
`=> x = 3/15 + 1/15 = 4/15`
Vậy `x = 4/15`
`-2/15 - x = -3/10`
`=> -x = 2/15 - 3/10`
`=> -x = 4/30 - 9/30`
`=> -x = -5/30 = -1/6`
`=> x = 1/6`
Vậy `x =1/6`
`x + 1/3 = 2/5 - (-1/3)`
`=> x + 1/3 = 2/5 + 1/3`
`=> x + 1/3 = 11/15`
`=> x = 11/15 - 1/3`
`=> x = 2/5`
Vậy `x = 2/5`
`3/7 - x = 1/4 - 3/5`
`=> 3/7 - x = -7/20`
`=> x = 3/7 - (-7/20)`
`=> x = 3/7 + 7/20`
`=> x = 109/140`
Vậy `x = 109/140`
`|x + 4/15| - |-3,75| = -|-2,15|`
`=> |x + 4/15| - 3,75 = -2,15`
`=> |x + 4/15| = -2,15 + 3,75 = 8/5`
`TH1: x + 4/15 = 8/5`
`=> x = 8/5 - 4/15= 4/3`
`TH2: x + 4/15 = -8/5`
`=> x = -8/5 - 4/15 = -28/15`
Vậy `x = {4/3 ; -28/15}`
`x - 3/4 <2/3`
`=> x < 2/3 + 3/4`
`=> x < 8/12 + 9/12`
`=> x < 17/12`
Vậy `x<17/12`
