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Ta có :
\(\frac{x+1}{49}+\frac{x+2}{48}+\frac{x+3}{47}+\frac{x+4}{46}+\frac{x+5}{45}=-5\)
\(\Leftrightarrow\)\(\left(\frac{x+1}{49}+1\right)+\left(\frac{x+2}{48}+1\right)+\left(\frac{x+3}{47}+1\right)+\left(\frac{x+4}{46}+1\right)+\left(\frac{x+5}{45}+1\right)=-5+5\)
\(\Leftrightarrow\)\(\frac{x+50}{49}+\frac{x+50}{48}+\frac{x+50}{47}+\frac{x+50}{46}+\frac{x+50}{45}=0\)
\(\Leftrightarrow\)\(\left(x+50\right)\left(\frac{1}{49}+\frac{1}{48}+\frac{1}{47}+\frac{1}{46}+\frac{1}{45}\right)=0\)
Vì \(\frac{1}{49}+\frac{1}{48}+\frac{1}{47}+\frac{1}{46}+\frac{1}{45}\ne0\)
Nên \(x+50=0\)
\(\Rightarrow\)\(x=-50\)
Vậy \(x=-50\)
Chúc bạn học tốt ~
\(a.3x-75=45+3\times\left(-25\right)\)
\(3x-75=45+\left(-75\right)\)
\(3x-75=-30\)
\(3x=-30+75\)
\(3x=45\)
\(x=45:3\)
\(x=15\)
Vậy \(x=15\)
\(b.\frac{x}{3}=\frac{2}{3}+\frac{-1}{7}\)
\(\frac{x}{3}=\frac{11}{21}\)
\(\Rightarrow\frac{x\times7}{21}=\frac{11}{21}\)
\(\Rightarrow x\times7=11\)
\(x=11:7\)
\(x=\frac{11}{7}\)
\(\Rightarrow\)\(x\)không thỏa mãn
Vậy \(x\in\varnothing\)
a) 3x-75=45+3.(-25)
\(\Rightarrow3x-75=45+\left(-75\right)\)
\(\Rightarrow3x-75-45+75=0\)
\(\Rightarrow3x-45-75+75=0\)
\(\Rightarrow3x-45=0\)
\(\Rightarrow3x=45\)
\(\Rightarrow x=\frac{45}{3}=15\)
Vậy: \(x=15\)
\(\frac{x+1}{49}+1+\frac{x+2}{48}+1+\frac{x+3}{47}+1+\frac{x+4}{46}+1+\frac{x+5}{45}+1=0\)
\(\Leftrightarrow\frac{x+50}{49}+\frac{x+50}{48}+...+\frac{x+50}{45}=0\)
\(\Leftrightarrow\left(x+50\right)\left(\frac{1}{49}+\frac{1}{48}+...+\frac{1}{45}\right)=0\)
Vì 1/49+1/48+...+1/45 khác 0
Nên x+50=0
do đó x=-50
-6/18 + 10/18 + 3/18 < x < 95/45 + 9/45 + 2/45
4/18 + 3/18 < x < 104/45 + 2/45
7/18 < x < 106/45
10/45 < x < 106/45
Vậy x = 11/45,12/45,13/45,.......,105/45
a) 3/2.x+1/2=1/10
Suy ra 3/2.x=1/10-1/2
hay 3/2.x=-4/10
Vậy x=-4/10 : 3/2 = -4/15
b) 1/90