a: \(x:\dfrac{1}{2}+\dfrac{5}{6}=\dfrac{7}{18}\)
=>\(x:\dfrac{1}{2}=\dfrac{7}{18}-\dfrac{5}{6}=\dfrac{7}{18}-\dfrac{15}{18}=-\dfrac{8}{18}=-\dfrac{4}{9}\)
=>\(x=-\dfrac{4}{9}\cdot\dfrac{1}{2}=-\dfrac{2}{9}\)
b: \(\dfrac{3}{2}x-\dfrac{3}{8}=\dfrac{9}{16}\)
=>\(\dfrac{3}{2}x=\dfrac{9}{16}+\dfrac{3}{8}=\dfrac{15}{16}\)
=>\(x=\dfrac{15}{16}:\dfrac{3}{2}=\dfrac{15}{16}\cdot\dfrac{2}{3}=\dfrac{5}{8}\)
c: \(\dfrac{3}{4}-\left|\dfrac{7}{2}-x\right|=-\dfrac{2}{5}\)
=>\(\left|\dfrac{7}{2}-x\right|=\dfrac{3}{4}+\dfrac{2}{5}=\dfrac{15}{20}+\dfrac{8}{20}=\dfrac{23}{20}\)
=>\(\left|x-\dfrac{7}{2}\right|=\dfrac{23}{20}\)
=>\(\left[{}\begin{matrix}x-\dfrac{7}{2}=\dfrac{23}{20}\\x-\dfrac{7}{2}=-\dfrac{23}{20}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{23}{20}+\dfrac{7}{2}=\dfrac{93}{20}\\x=-\dfrac{23}{20}+\dfrac{7}{2}=\dfrac{47}{20}\end{matrix}\right.\)
`x : 1/2 + 5/6 = 7/18`
`=> x : 1/2 = 7/18 - 5/6`
`=> x : 1/2 = -4/9`
`=> x = - 4/9 xx 1/2 `
`=> x = -2/9`
`b) 3/2 xx x - 3/8 = 9/16`
`=> 3/2 xx x= 9/16 +3/8`
`=> 3/2 xx x = 15/16`
`=> x = 15/16 :3/2`
`=> x =5/8`
`c) 3/4 - |7/2 - x| = -2/5`
`=> |7/2 - x | = 3/4 + 2/5`
`=> |7/2 - x| = 23/20`
TH1:
`7/2 - x = 23/20`
`=> x = 7/2 - 23/20`
`=> x = 47/20`
TH2:
`7/2 - x = -23/20`
`=> x = 7/2 + 23/20`
`=> x = 93/20`
