Tìm x , biết : a,| x – $\frac{5}{3}$ | < $\frac{1}{3}$ b, | x + $\frac{11}{2}$ | > | -5,5| c, $\frac{2}{5}$ < | x - $\frac{7}{5}$ < $\frac{3}{5}$

Đáp án:

Giải thích các bước giải:

`a)|x-5/3|<1/3`

`=>-1/3<x-5/3<1/3`

`=>-1/3+5/3<x<1/3+5/3`

`=>4/3<x<2`

`b)`

`|x+11/2|>|-5,5|`

`=>|x+11/2|>5,5`

`=>|x+11/2|>11/2`

`=>`\(\left[ \begin{array}{l}x+\dfrac{11}{2}>\dfrac{11}{2}\\x+\dfrac{11}{2}<-\dfrac{11}{2}\end{array} \right.\)

`=>`\(\left[ \begin{array}{l}x>0\\x<-11\end{array} \right.\)

`c)`

`2/5<|x-7/5|<3/5`

$\bullet$

`2/5<|x-7/5|`

`=>`\(\left[ \begin{array}{l}x-\dfrac{7}{5}>\dfrac{2}{5}\\x-\dfrac{7}{5}<-\dfrac{2}{5}\end{array} \right.\)

`=>`\(\left[ \begin{array}{l}x>\dfrac{9}{5}\\x<-1\end{array} \right.\)

$\bullet$

`|x-7/5|<3/5`

`=>-3/5<x-7/5<3/5`

`=>-3/5+7/5<x<3/5+7/5`

`=>4/5<x<2`

Từ hai điều kiện trên `=>9/5<x<2`