\(=>x\left(\dfrac{1}{2}+\dfrac{2}{3}\right)=\dfrac{10}{3}+1=\dfrac{13}{3}\)

\(=>x=\dfrac{13}{3}:\left(\dfrac{1}{2}+\dfrac{2}{3}\right)=\dfrac{13}{3}:\dfrac{7}{6}=\dfrac{26}{7}\)

5/6x - 1 = 10/3

5/6x = 10/3 + 1 = 13/3

X = 13/3 : 5/6 = 26/5

\(\dfrac{1}{2}\times x+\dfrac{2}{3}\times x-1=3\dfrac{1}{3}\)

\(\Rightarrow x\left(\dfrac{1}{2}+\dfrac{2}{3}\right)=\dfrac{10}{3}+1\)

\(\Rightarrow\dfrac{7}{6}x=\dfrac{13}{3}\)

\(\Rightarrow x=\dfrac{13}{3}:\dfrac{7}{6}\)

\(\Rightarrow x=\dfrac{26}{7}\)

a)x+x+2.x=76:2

=>2x+2x=38

=>2(x+x)=38

=>2x=19

=>x=19/2

b)2.x=x+14

=>2x-x=14

=>x=14

c)2.x-3/5=3/4

=>2x=3/4+3/5

=>2x=27/20

=>x=27/40

d)3/5-2.x=1/4

=>2x=3/5-1/4

=>2x=7/20

=>x=7/40

/2.x-3/=x-1 \(\Leftrightarrow\orbr{\begin{cases}2x-3=x-1\\2x-3=-(x-1)\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}2x-3-x=-1\\2x-3=-x+1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x(2-1)=2\\2x+x=4\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2\\3x=4\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=2\\x=\frac{4}{3}\end{cases}}}\)

\(∘backwin\)

\(a ) ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ... + ( x + 100 ) = 5750\)

\( ( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 100 ) = 5750 \)

\( 100 x + ( 1 + 100 ) ×100 : 2 = 5750\)

\(100 x + 5050 = 5750\)

\( 100 x = 5750 − 5050\)

\(100 x = 700\)

\(x = 700 : 100\)

\(x = 7\)

\(b,\) \(B=\)\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{2021^2}< \dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2020}+2021\)

\( B < 1 -\)\(\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2020}-\dfrac{1}{2021}\)

\(B<1-\)\(\dfrac{1}{2021}\)

\(B<\)\(\dfrac{2020}{2021}\)

\(\dfrac{2020}{2021}< 1\)

\(B<1\)

a) (x+1) +(x+2 ) + ...+(x+100)=5750
= 100x + (1+2+3+...+100) = 5750
=100x + 5050 = 5750
--> 100x = 5750-5050=700
--> x=7

b) Ta thấy: 1/2^2 < 1/2.3
                  1/3^2 < 1/3.4
                        ...
                  1/2021^2 < 1/2021.2022
--> B=1/2^2 + 1/3^2 + 1/4^2 + ...+ 1/2021^2 < 1/2.3 + 1/3.4 + ... +1/2021.2022 (1)
     Ta có: 1/2.3 + 1/3.4 + ... +1/2021.2022
         =1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2021 - 1/2022
         =1/2 - 1/2022 < 1 (2)
Từ (1) và (2) --> B<1 (đpcm)
                                                                      < 
                                                                     

a. 3^x=1-x^2

x=0 la nghiem

x>=1;  VT>=3 VP<=0 vo nghiem 

b. (de bai thieu n khac 0 vi neu n=0 dung voi moi x)

3x-14=1=> x=5

c.(5^2x5^^x+1)=5^4

5^{^x+1}=5^2=> x=1

dễ :>>

\(x+\frac{4}{9}=\frac{1}{2}\)

\(x=\frac{1}{2}-\frac{4}{9}\)

\(x=\frac{9}{18}-\frac{8}{18}\)

\(x=\frac{1}{18}\)