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Dùng công thức tính tổng
\(1+2+3+...+x=11325\)
\(\Leftrightarrow\frac{x\left(x+1\right)}{2}=11325\)
\(\Leftrightarrow x\left(x+1\right)=22650\)
\(\Leftrightarrow x\left(x+1\right)=150.151\)
Nên x = 150
Vậy ,,,
\(1+2+3+4+...+x=11325\)
\(\Rightarrow\frac{x\left(x+1\right)}{2}=11325\)
\(\Rightarrow x\left(x+1\right)=11325\times2\)
\(\Rightarrow x\left(x+1\right)=22650\)
\(\Rightarrow150\times151=22650\)
\(\Rightarrow x=150\)

a, 1 + 3 + 5 + 7 + ............. + n
=\(\frac{\left(n+1\right)\left(n-1\right)}{2}\)=676
=>\(\left(n+1\right)\left(n-1\right)\)=676*2 =1352
Còn lạ bạn tự suy luận là ra
[1+n].n:2=676
[1+n].n=1352=35.37
n=20
[2+n].n:2=992
[2+n].n=1984=42.44
n=44

1, 15+(20-35)
=15+(-15)
=0
2,37.24+76.37
=37(24+76)
=37.100
=3700
3,420:{30:[260-(91.5-\(2^3\).\(5^2\))]}
=420:{30:[260-(455-200)
=420:[30:(260-455+200)
=420:(30:5)
=420:6
=70
5,2(x-11):3=56
<=>2(x-11)=56.3
<=>2(x-11)=168
<=>x-11=168:2
<=>x-11=84
<=>x=84+11
<=>x=95
Vậy x=95

\(\frac{7}{4}.x-\frac{3}{2}=\frac{1}{2}x-3\)
\(\Rightarrow\frac{7}{4}x-\frac{1}{2}x=\frac{3}{2}-3\)
\(\Rightarrow\frac{5}{4}x=-\frac{3}{2}\)
\(\Rightarrow x=-\frac{3}{2}.\frac{4}{5}=-\frac{6}{5}\)
7x/4-3/2=x/2-3
=> 7x/4-6/4=x/2-6/2
=>7x-6/4=x-6/2
=>(7x-6)*2=(x-6)*4
=>14x-12=4x-24
=>10x=-24+12
=>10x=-12=>x=-6/5
Vậy x=-6/5
Ta có: \(2\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|-\dfrac{3}{2}=\dfrac{1}{4}\)
\(\Leftrightarrow2\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{7}{4}\)
\(\Leftrightarrow\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{7}{8}\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{7}{8}\\\dfrac{1}{2}x-\dfrac{1}{3}=-\dfrac{7}{8}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x=\dfrac{29}{24}\\\dfrac{1}{2}x=-\dfrac{13}{24}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{29}{12}\\x=-\dfrac{13}{12}\end{matrix}\right.\)