Question

3/4 - |4/5-x| = -1

Answer 1

\(\dfrac{3}{4}-\left|\dfrac{4}{5}-x\right|=-1\)

* Nếu \(\dfrac{4}{5}-x\ge0\Leftrightarrow x\le\dfrac{4}{5}\)

\(\dfrac{3}{4}-\left(\dfrac{4}{5}-x\right)=-1\)

\(\dfrac{3}{4}-\dfrac{4}{5}+x=-1\)

\(x=-1-\dfrac{3}{4}+\dfrac{4}{5}\)

\(x=-\dfrac{20}{20}-\dfrac{15}{20}+\dfrac{16}{20}\)

\(x=-\dfrac{19}{20}\)(TMĐK)

* Nếu \(\dfrac{4}{5}-x< 0\Leftrightarrow x>\dfrac{4}{5}\)

\(\dfrac{3}{4}-\left[-\left(\dfrac{4}{5}-x\right)\right]=-1\)

\(\dfrac{3}{4}-\left(-\dfrac{4}{5}+x\right)=-1\)

\(\dfrac{3}{4}+\dfrac{4}{5}-x=-1\)

\(-x=-1-\dfrac{3}{4}-\dfrac{4}{5}\)

\(-x=-\dfrac{20}{20}-\dfrac{15}{20}-\dfrac{16}{20}\)

\(-x=-\dfrac{51}{20}\)

\(x=\dfrac{51}{20}\)(TMĐK)

Answer 2

3/4 - | 4/5 - x | = -1

<=> 4/5 - x = 3/4 - ( -1)

<=> 4/5 - x = 3/4 + 1

<=> 4/5 - x = 7/4

<=> 4/5 - x = 7/4

hoặc 4/5 - x = -7/4

<=> x = 4/5 - 7/4

hoặc x = 4/5 - ( -7/4 )

<=> x = -19/20

hoặc x = 51/20

Vậy x = -19/20 , x = 51/20.

Answer 3

\(\dfrac{3}{4}-\left|\dfrac{4}{5}-x\right|=-1\)

\(\left|\dfrac{4}{5}-x\right|=\dfrac{3}{4}+1\) =>\(\left|\dfrac{4}{5}-x\right|=\dfrac{7}{4}\)

=> \(\dfrac{4}{5}-x=\dfrac{7}{4}Hay\dfrac{4}{5}-x=\dfrac{-7}{4}\)

Với \(\dfrac{4}{5}-x=\dfrac{7}{4}\) Với \(\dfrac{4}{5}-x=\dfrac{-7}{4}\)

\(x=\dfrac{4}{5}-\dfrac{7}{4}\) \(x=\dfrac{4}{5}+\dfrac{7}{4}\)

\(x=\dfrac{-19}{20}\) \(x=\dfrac{51}{20}\)