Question

Tính:

a) \(6-\left|\dfrac{1}{2}-x\right|=\dfrac{2}{5}\)

b)\(2-\left|x-\dfrac{2}{5}\right|=-\dfrac{1}{2}\)

Answer 1

a: =>|x-1/2|=6-2/5=28/5

=>x-1/2=28/5 hoặc x-1/2=-28/5

=>x=61/10 hoặc x=-51/10

b: =>|x-2/5|=2+1/2=5/2

=>x-2/5=5/2 hoặc x-2/5=-5/2

=>x=29/10 hoặc x=-21/10

Answer 2

`a)6-|1/2-x|=2/5`

`|1/2-x|=6-2/5=28/5`

`@1/2-x=28/5=>x=1/2-28/5=-51/10`

`@1/2-x=-28/5=>x=1/2-(-28/5)=61/10`

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`b)2-|x-2/5|=-1/2`

`|x-2/5|=2-(-1/2)=5/2`

`@x-2/5=5/2=>x=5/2+2/5=29/10`

`@x-2/5=-5/2=>x=-5/2+2/5=-21/10`

Answer 3

a) `6 - | 1/2 - x | = 2/5`

`<=> |1/2 - x| = 6 - 2/5 = 28/5`

`<=>`\(\left[{}\begin{matrix}\dfrac{1}{2}-x=\dfrac{28}{5}\\\dfrac{1}{2}-x=-\dfrac{28}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{51}{10}\\x=\dfrac{61}{10}\end{matrix}\right.\)

b)`2-|x-2/5| = -1/2`

`<=> |x-2/5| = 2 + 1/2 = 5/2`

`<=>`\(\left[{}\begin{matrix}x-\dfrac{2}{5}=\dfrac{5}{2}\\x-\dfrac{2}{5}=-\dfrac{5}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{29}{10}\\x=-\dfrac{21}{10}\end{matrix}\right.\)

Answer 4

`6 - | 1/2 - x| = 2/5`

`|1/2-x| = 6 - 2/5`

`|1/2 - x| =28/5`

`=>` \(\left[{}\begin{matrix}\dfrac{1}{2}-x=\dfrac{28}{5}\\\dfrac{1}{2}-x=-\dfrac{28}{5}\end{matrix}\right.\)

`=>` \(\left[{}\begin{matrix}x=\dfrac{1}{2}-\dfrac{28}{5}\\x=\dfrac{1}{2}-\left(-\dfrac{28}{5}\right)\end{matrix}\right.\)

`=>` \(\left[{}\begin{matrix}x=\dfrac{1}{2}-\dfrac{28}{5}\\x=\dfrac{1}{2}+\dfrac{28}{5}\end{matrix}\right.\)

`=>` \(\left[{}\begin{matrix}x=-\dfrac{51}{10}\\x=\dfrac{61}{10}\end{matrix}\right.\)

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`2-| x - 2/5| = -1/2`

`|x-2/5| = 2 - (-1/2)`

`|x-2/5| = 2 + 1/2`

`|x-2/5| = 5/2`

`=>` \(\left[{}\begin{matrix}x-\dfrac{2}{5}=\dfrac{5}{2}\\x-\dfrac{2}{5}=-\dfrac{5}{2}\end{matrix}\right.\)

`=>` \(\left[{}\begin{matrix}x=\dfrac{5}{2}+\dfrac{2}{5}\\x=-\dfrac{5}{2}+\dfrac{2}{5}\end{matrix}\right.\)

`=>` \(\left[{}\begin{matrix}x=\dfrac{29}{10}\\x=-\dfrac{21}{10}\end{matrix}\right.\)