Question

Tìm x biết:

\(a) x+2x+3x+4x+...+100x=-213\)

\(b) \frac12 x-\frac13=\frac14-4\frac16\)

\(c)3(x-2)+2(x-1)=10\)

\(d)\frac{\mathrm x+1}{\mathrm3}=\frac{\mathrm x-2}{\mathrm4}\)

Answer 1

a) \(x+2x+3x+...+100x=-213\)

\(\Rightarrow x.\left(1+2+3+...+100\right)=-213\)

\(\Rightarrow x.5050=-213\Rightarrow x=\frac{-213}{5050}\)

b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}-4\frac{1}{6}\)

\(\Rightarrow\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}-\frac{25}{6}\)

\(\Rightarrow\frac{1}{2}x-\frac{1}{3}=\frac{-47}{12}\)

\(\Rightarrow\frac{1}{2}x=\frac{-43}{12}\Rightarrow x=\frac{-43}{6}\)

d) \(\frac{x+1}{3}=\frac{x-2}{4}\Rightarrow4\left(x+1\right)=3\left(x-2\right)\Rightarrow4x+4=3x-6\)

                                                                    \(\Rightarrow4x-3x=-6-4\Rightarrow x=-10\)

c) \(3\left(x-2\right)+2\left(x-1\right)=10\)

\(\Rightarrow3x-6+2x-2=10\)

\(\Rightarrow5x=18\Rightarrow x=\frac{18}{5}\)

Answer 2

a) \(x+2x+3x+4x+...+100x=-213\)

\(x.\left(1+2+3+4+...+100\right)=-213\)

\(x.5050=-213\)

\(x=-\frac{213}{5050}\)

b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}-4\frac{1}{6}\)

\(\frac{1}{2}x-\frac{1}{3}=-\frac{47}{12}\)

\(\frac{1}{2}x=-\frac{43}{12}\)

\(x=\frac{-43}{6}\)

Answer 3

c) \(3\left(x-2\right)+2\left(x-1\right)=10\)

\(3x-6+2x-2=10\)

\(3x+2x-\left(6+2\right)=10\)

\(5x-8=10\)

\(5x=18\)

\(x=\frac{18}{5}\)

d) \(\frac{x+1}{3}=\frac{x-2}{4}\)

\(\Rightarrow4.\left(x+1\right)=3\left(x-2\right)\)

\(4x+4=3x-6\)

\(\Rightarrow4x-3x=-6-4\)

\(x=-10\)