Toán Lớp 7: 1/4 – ( x + 5/2 ) = – | – 3/2 |
| x – 2021 | + | 2021 – x | = 2020
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Toán Lớp 7: 1/4 – ( x + 5/2 ) = – | – 3/2 |
| x – 2021 | + | 2021 – x | = 2020
Comments ( 2 )
$\dfrac{1}{4}-\left(x+\dfrac{5}{2}\right)=-\left|-\dfrac{3}{2}\right|$
$⇒\dfrac{1}{4}-\left(x+\dfrac{5}{2}\right)-\dfrac{1}{4}=-\left|-\dfrac{3}{2}\right|-\dfrac{1}{4}$
$⇒-\left(x+\dfrac{5}{2}\right)=-\dfrac{7}{4}$
$⇒\dfrac{-\left(x+\dfrac{5}{2}\right)}{-1}=\dfrac{-\dfrac{7}{4}}{-1}$
$⇒\dfrac{2x+5}{2}=\dfrac{7}{4}$
$⇒\dfrac{2\left(2x+5\right)}{2}=\dfrac{7\cdot \:2}{4}$
$⇒2x+5=\dfrac{7}{2}$
$⇒2x+5-5=\dfrac{7}{2}-5$
$⇒2x=-\dfrac{3}{2}$
$⇒\dfrac{2x}{2}=\dfrac{-\dfrac{3}{2}}{2}$
$⇒x=-\dfrac{3}{4}$
Vậy $x=-\dfrac{3}{4}$
$—————————$
$\left|x-2021\right|+\left|2021-x\right|=2020$
⇒abs(x – 2021) = 1010
⇒sqrt((2021 – x)^2) + sqrt((x – 2021)^2) = 2020
$⇒2\left|2021-x\right|=2020$
$⇒\dfrac{2\left|2021-x\right|}{2}=\dfrac{2020}{2}$
$⇒\left|2021-x\right|=1010$
\(⇒\left[ \begin{array}{l}2021-x=-1010\\\:2021-x=1010\end{array} \right.\) \(⇒\left[ \begin{array}{l}x=1011\\x=3031\end{array} \right.\)
Vậy $x=1011\quad \mathrm{hoặc}\quad \:x=3031$
Lời giải và giải thích chi tiết:
a)
1/4-(x+5/2)=-|-3/2|
=>1/4-(x+5/2)=-3/2
=>x+5/2=1/4+3/2
=>x+5/2=1/4+6/4
=>x+5/2=7/4
=>x=7/4-5/2
=>x=14/8-20/8
=>x=-6/8
=>x=-3/4
Vậy x=-3/4
b)
|x-2021|+|2021-x|=2020
=>|x-2021|+|-(x-2021)|=2020
=>|x-2021|+|x-2021|=2020
=>2.|x-2021|=2020
=>|x-2021|=2020:2
=>|x-2021|=1010
=>[(x-2021=1010),(x-2021=-1010):}
=>[(x=1010+2021),(x=-1010+2021):}
=>[(x=3031),(x=1011):}
Vậy x\in{3031;1011}