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\(a,\)\(71+65\times4=\frac{x+140}{x}+260\)
\(\Rightarrow71+260=\frac{x-140}{x}+260\)
\(\Rightarrow71=\frac{x-140}{x}\)
\(\Rightarrow71x=x-140\)
\(\Rightarrow71x-x=-140\)
\(\Rightarrow70x=-140\)
\(\Rightarrow x=-2\)
\(b,\)\(y\times\frac{15}{2}-\frac{1}{3}\times\left(\frac{1}{4}+y\right)=90\frac{2}{3}\)
\(\Rightarrow\frac{15y}{2}-\frac{1}{12}-\frac{y}{3}=\frac{272}{3}\)
\(\Rightarrow\frac{90y}{12}-\frac{1}{12}-\frac{4y}{12}=\frac{1088}{12}\)
\(\Rightarrow90y-1-4y=1088\)
\(\Rightarrow86y=1089\)
\(\Rightarrow y=\frac{1089}{86}\)

a) \(\left(x+1\right)+\left(x+4\right)+\left(x+7\right)+...+\left(x+28\right)=155\)
\(\Rightarrow10\times x+\left(1+4+7+...+28\right)=155\)
\(\Rightarrow10\times x+\frac{\left(1+28\right)\times10}{2}=155\)
\(\Rightarrow10\times x+145=155\)
\(\Rightarrow10\times x=10\Rightarrow x=1\)
b)

\(a̸\)
\(\frac{3}{5}-\frac{1}{2}.x=\frac{1}{4}\)
\(\frac{1}{2}.x=\frac{3}{5}-\frac{1}{4}\)
\(\frac{1}{2}.x=\frac{7}{20}\)
\(\Rightarrow\frac{7}{10}\)
\(b̸\)
\(11,3+2\left[x-\frac{1}{3}\right]=\frac{25}{6}\)
\(2\left[x-\frac{1}{3}\right]=\frac{25}{6}-11,3\)
\(2\left[x-\frac{1}{3}\right]=\frac{-107}{15}\)
\(x-\frac{1}{3}=\frac{-107}{15}:2\)
\(x-\frac{1}{3}=\frac{-107}{30}\)
\(x=\frac{-107}{30}+\frac{1}{3}\)
\(x=\frac{-97}{30}\)
\(a)\frac{3}{5}-\frac{1}{2}x=\frac{1}{4}\)
\(\implies\frac{1}{2}x=\frac{3}{5}-\frac{1}{4}\)
\(\implies\frac{1}{2}x=\frac{7}{20}\)
\(\implies x=\frac{7}{20}:\frac{1}{2}\)
\(\implies x=\frac{7}{10}\)
Vậy...
\(b) 11,3+2(x-\frac{1}{3})=\frac{25}{6}\)
\(\implies \frac{113}{10}+2x-2.\frac{1}{3}=\frac{25}{6}\)
\(\implies \frac{113}{10}+2x-\frac{2}{3}=\frac{25}{6}\)
\(\implies \frac{113}{10}+2x=\frac{25}{6}+\frac{2}{3}\)
\(\implies \frac{113}{10}+2x=\frac{29}{6}\)
\(\implies 2x=\frac{29}{6}-\frac{113}{10}\)
\(\implies 2x=\frac{-97}{15}\)
\(\implies x=\frac{-97}{30}\)
Vậy..
\(c)5x-435+2x+140+3x=565\)
\(\implies (5x+2x+3x)+(-435+140)=565\)
\(\implies 10x+(-295)=565\)
\(\implies 10x=565-(-295)\)
\(\implies 10x=860\)
\(\implies x=86\)
Vậy...
~ hok tốt a~

Ta có (x + 1) + (x + 2) + .......... + ( x + 9) = 545
<=> (x + x + x + ....... + x) + ( 1 + 2 + ...... + 9) = 545
<=> 9x + 45 = 545
=> 9x = 500
=> x = 500/9

140:(2x+1)=4
2x+1=35
2x=34
x=17
Vậy x=17
Học tốt!
140 : (2xX + 1)=4
2 x X + 1 =140 : 4
2 x X + 1=35
2 x X = 35 - 1
2 x X = 34
X= 34 : 2
X= 17
Vậy : X= 17