(x+1)+(x-2)+(x+3)+(x-4)...(x-50)=-175
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\(a,50\%x-0,2+x=\dfrac{4}{5}\)
\(\Leftrightarrow\dfrac{1}{2}x-0,2+x=\dfrac{4}{5}\)
\(\Leftrightarrow\dfrac{1}{2}x+x=\dfrac{4}{5}+0,2\)
\(\Leftrightarrow\dfrac{3}{2}x=\dfrac{4}{5}+\dfrac{1}{5}\)
\(\Leftrightarrow\dfrac{3}{2}x=1\)
\(\Leftrightarrow x=\dfrac{2}{3}\)
\(b,\left(x-\dfrac{3}{4}\right):\dfrac{1}{2}+\dfrac{3}{2}=\dfrac{25}{2}\)
\(\Leftrightarrow\left(x-\dfrac{3}{4}\right).2=\dfrac{25}{2}-\dfrac{3}{2}\)
\(\Leftrightarrow\left(x-\dfrac{3}{4}\right).2=\dfrac{22}{2}\)
\(\Leftrightarrow x-\dfrac{3}{4}=11:2\)
\(\Leftrightarrow x=\dfrac{11}{2}+\dfrac{3}{4}\)
\(\Leftrightarrow x=\dfrac{25}{4}\)
A.\(\left(\frac{4}{7}.x-1\right).3=\frac{1}{21}\)
\(\frac{4}{7}.x-1=\frac{1}{21}:3\)
\(\frac{4}{7}.x-1=\frac{1}{21}.3\)
\(\frac{4}{7}.x-1=\frac{1}{7}\)
\(\frac{4}{7}.x=1+\frac{1}{7}\)
\(\frac{4}{7}.x=\frac{8}{7}\)
\(x=\frac{8}{7}:\frac{4}{7}\)
\(x=\frac{8}{7}.\frac{7}{4}\)
\(x=2\)
Vậy x=2
C.\(\frac{2}{3}.x-\frac{1}{3}.x=\frac{5}{9}\)
\(\left(\frac{2}{3}-\frac{1}{3}\right).x=\frac{5}{9}\)
\(\frac{1}{3}.x=\frac{5}{9}\)
\(x=\frac{5}{9}:\frac{1}{3}\)
\(x=\frac{5}{9}.3\)
\(x=\frac{5}{3}\)
Vậy \(x=\frac{5}{3}\)
D. \(\left(x-2\frac{1}{4}\right).\left(\frac{-2}{3}\right).50\%=2\frac{5}{6}\)
\(x.\frac{-2}{3}-\frac{9}{4}.\frac{-2}{3}=\frac{17}{6}:\frac{1}{2}\)
\(x.\frac{-2}{3}-\frac{-3}{2}=\frac{17}{6}.2\)
\(x.\frac{-2}{3}+\frac{3}{2}=\frac{17}{3}\)
\(x.\frac{-2}{3}=\frac{17}{3}-\frac{3}{2}\)
\(x.\frac{-2}{3}=\frac{34}{6}-\frac{9}{6}\)
\(x.\frac{-2}{3}=\frac{25}{6}\)
\(x=\frac{25}{6}:\frac{-2}{3}\)
\(x=\frac{25}{6}.\frac{3}{-2}\)
\(x=\frac{25}{-4}\)
Vậy \(x=\frac{25}{-4}\)
\(C=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.....\dfrac{48}{49}.\dfrac{49}{50}=\dfrac{1}{50}\)
Do x1+x2=x3+x4=...=x49+x50=1 => x1+x2+x3+x4+...+x49+x50=1.50/2=25.
Mặt khác, x1+x2+x3+x4+...+x49+x50+x51=0 => x51=0-25=-25
tổng x1+x2+........+x50 là :
x1+x2+......+x50 =(x1+x2)+....+(x49+x50)=1+1+.....+1=25
ta co :
25+x51=0
x51=0-25
x51 =-25
Vay x51 =-25
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b)0,5x+2/3x+2/3=7/2
1/2x+2/3x+2/3=7/2
x(1/2+2/3)+2/3=7/12
x.7/6+2/3 =7/12
x.7/6 =7/12-2/3
x.7/6 =-1/12
x =-1/12:7/6
x =-1/14
b)3/5-2/15:x=1/2
2/15:x =3/5-1/2
2/15:x =1/10
x =2/15:1/10
x = 4/3
60 -3(x-3) = 51 (x + 2) + ( x + 4) + ( x + 6) + ....+ ( x +50) = 750
=> 3(x-3) = 60 - 51 Số số hạng của dãy 2 ; 4 ; 6 ; ....; 50 là:
=> 3(x-3) = 9 ( 50 - 2) : 2 + 1 = 25 ( số)
=> x -3 = 9 : 3 Tổng của dãy trên là : ( 50 + 2) . 25 : 2 = 650
=> x-3 = 3 Ta có : ( x + x +x +x +...+x) + 650 = 750
=> x = 3 + 3 25x
=> x = 6 => 25x + 650 = 750
=> 25x = 750 - 650
=> 25x = 100
=> x = 100 : 25
=> x = 4
\(\left(x+1\right)+\left(x-2\right)+\left(x+3\right)+\left(x-4\right)...\left(x-50=-175\right)\)
\(\Rightarrow x+1+x-2+x+3+x-4+...+x-50=-175\)
\(\Rightarrow\left(x+x+...+x\right)+\left(1-2+3-4+...-50\right)=-175\)
\(\Rightarrow50x+\left(1-2\right)+\left(3-4\right)+...+\left(49-50\right)=-175\)
\(\Rightarrow50x+\left(-1\right)+\left(-1\right)+...+\left(-1\right)=-175\)
\(\Rightarrow50x+\left(-1\right)50=-175\)
\(\Rightarrow50x+\left(-50\right)=-175\)
\(\Rightarrow50x=-175+50=-125\)
\(\Rightarrow x=-125\div50=\frac{-5}{2}\)
(x+1)+(x-2)+(x+3)+(x-4)+...+(x-50)=-175
x+1+x-2+x+3+x-4+...+x-50=-175
50x+(1-2+3-4+...+49-50)=-175
50x-25=-175
50x=-150
x=-3