Toán Lớp 7: |2019-x|+|2020-x|=x-2021 Tìm x

Question

Toán Lớp 7:  |2019-x|+|2020-x|=x-2021 Tìm x

haianhtu97 · Answer

| 2019 - x | + | 2020 - x | = x - 2021  (1)    Ta c&oacute; :    $ left. begin{matrix} | 2019 - x |  ge 0 với  forall x   | 2020 - x |  ge 0 với  forall x  end{matrix} right }$    $ Rightarrow$ | 2019 - x | + | 2020 - x | $ ge$ 0 $ forall$ x   $ Rightarrow$ x - 2021 $ ge$ 0 $ forall$ x   $ Rightarrow$ x $ ge$ 2021   $ Rightarrow$ $ begin{cases} 2019 - x < 0   2020 - x < 0 end{cases}$          $ Rightarrow$ $ begin{cases} | 2019 - x | = -( 2019 - x )   | 2020 - x | = - ( 2020 - x ) end{cases}$                   $ Rightarrow$ $ begin{cases} | 2019 - x | = x - 2019   | 2020 - x | = x - 2020 end{cases}$   Thay v&agrave;o (1), ta đc :   ( x - 2019 ) +  ( x - 2020 ) = x - 2021   $ Rightarrow$ x - 2019 + x - 2020 = x - 2021   $ Rightarrow$ ( x + x ) - ( 2019 + 2020 ) = x - 2021   $ Rightarrow$ 2x - 4039 = x - 2021   $ Rightarrow$       2x      = x - 2021 + 4039   $ Rightarrow$       2x       = x + 2018   $ Rightarrow$        x        = 2018           Vậy x = 2018