Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
#)Giải :
a) x + 2x + 3x + ... + 100x = - 213
=> 100x + ( 2 + 3 + 4 + ... + 100 ) = - 213
=> 100x + 5049 = - 213
<=> 100x = - 5262
<=> x = - 52,62
#)Giải :
b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}x-\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{3}+\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{2}\)
\(\Rightarrow\left(\frac{1}{2}+\frac{1}{4}\right)x=\frac{1}{2}\)
\(\Rightarrow\frac{3}{4}x=\frac{1}{2}\)
\(\Leftrightarrow x=\frac{2}{3}\)
a: \(\dfrac{x-6}{7}+\dfrac{x-7}{8}+\dfrac{x-8}{9}=\dfrac{x-9}{10}+\dfrac{x-10}{11}+\dfrac{x-11}{12}\)
\(\Leftrightarrow\left(\dfrac{x-6}{7}+1\right)+\left(\dfrac{x-7}{8}+1\right)+\left(\dfrac{x-8}{9}+1\right)=\left(\dfrac{x-9}{10}+1\right)+\left(\dfrac{x-10}{11}+1\right)+\left(\dfrac{x-11}{12}+1\right)\)
=>x+1=0
hay x=-1
c: |x-2|=13
=>x-2=13 hoặc x-2=-13
=>x=15 hoặc x=-11
d: \(\Leftrightarrow3\left|x-2\right|+4\left|x-2\right|=2-\dfrac{1}{3}=\dfrac{5}{3}\)
=>7|x-2|=5/3
=>|x-2|=5/21
=>x-2=5/21 hoặc x-2=-5/21
=>x=47/21 hoặc x=37/21
a) \(\frac{x+1}{3}=\frac{x-2}{4}\)
=> (x+1).4 = (x - 2) . 3
=> 4x + 4 = 3x - 6
=> 4x - 3x = - 6 - 4
=> x = - 10
b) \(\frac{x-6}{7}+\frac{x-7}{8}+\frac{x-8}{9}=\frac{x-9}{10}+\frac{x-10}{11}+\frac{x-11}{12}\)
\(\Rightarrow\left(\frac{x-6}{7}+1\right)+\left(\frac{x-7}{8}+1\right)+\left(\frac{x-8}{9}+1\right)=\left(\frac{x-9}{10}+1\right)+\left(\frac{x-10}{11}+1\right)+\left(\frac{x-11}{12}+1\right)\)
\(\Rightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}=\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}\)
\(\Rightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}-\frac{x+1}{10}-\frac{x+1}{11}-\frac{x+1}{12}\) = 0
\(\Rightarrow\left(x+1\right).\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\right)\)
Vì \(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\ne0\) nên x + 1 =0
=> x = -1
c) Xem lại đề
\(\text{a, 3(x+1)+4x=10}\)
\(\Rightarrow3x+3+4x=10\)
\(\Rightarrow7x+3=10\)
\(\Rightarrow7x=10-3=7\)
\(\Rightarrow x=1\)
c, x+1/10+x+2/9=x+3/8+x+4/7
=> (x+1/10 +1) +(x+2/9 +1)= ( x+3/8 +1) +(x+4/7 +1)
=> x+11/10 + x+11/9 = x+11/8 + x+11/7
...............
a) \(3\left(x+1\right)+4x=10\)
\(\Rightarrow3x+3+4x=10\)
\(\Rightarrow3x+4x=10-3\)
\(\Rightarrow7x=7\)
\(\Rightarrow x=7\)
8 ) | x + 12 | - 12 = 1
\(|x+12|=13\)
\(\Rightarrow\orbr{\begin{cases}x+12=13\\x+12=-13\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=1\\x=-25\end{cases}}\)
Vậy \(x\in\left\{1;-25\right\}\)
9) 135 -\(|9-x|=35\)
\(|9-x|=135-35\)
\(|9-x|=100\)
\(\Rightarrow\orbr{\begin{cases}9-x=100\\9-x=-100\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-91\\x=109\end{cases}}\) Vậy x\(\in\left\{-91;109\right\}\) 10) 17+x-(352-400)=-32 17+x-352+400=-32 17+x-352 =(-32) - 400 17+x-352 =-432 17+x =(-432) + 352 17+x =-80 x =(-80) - 17 x =-97 Vậy x =-97 11) 2130 - (x+136) + 72 =-64 2130 - (x+136) =(-64) -72 2130 - (x+136) =-136 (x +136) = 2130 -(-136) x+136 =2266 x =2266 - 136 x =2130 Vậy x=2130 do sap an cơm nên chiều mình sẽ giải tiếp nha! sorryy
12) (x-2) - (-8) = -137
(x-2) +8 =-137
(x-2) =(-137) - 8
x-2 =-145
Vậy x=-145
13) 10-\(|x+3|=-4.\left(-10\right)\) 10- \(|x+3|=40\) \(|x+3|=\) 40+10 \(|x+3|=50\)
\(\Rightarrow\orbr{\begin{cases}x+3=50\\x+3=-50\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=50-3\\x=\left(-50\right)-3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=20\\x=-53\end{cases}}\)
Vậy x\(\in\left\{20;-53\right\}\)