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a) ( 2x + 1 ) . 2907 = 8 721
2x + 1 = 3
2x = 2
x = 1

g)\(2907\left(2x+1\right)=8721\)
⇔\(2x+1=3\)
⇔\(2x=2\)
⇔\(x=1\)
h)\(\left(4x-16\right):1905=60\)
⇔\(4x-16=114300\)
⇔\(4x=114316\)
⇔\(x=28579\)
i)\(23+3x=5^6:5^3\)
⇔\(23+3x=5^3\)
⇔\(23+3x=125\)
⇔\(3x=102\)
⇔\(x=34\)
k)\(219-7\left(x+1\right)=100\)
⇔\(7\left(x+1\right)=119\)
⇔\(x+1=17\)
⇔\(x=16\)

a)-(-2907)+(777-2900)
=2907+(-2123)
=784
b)714-38-262+106
=676-262+106
=414+106
=520

x + 1234 - 532 = 2907
x + 1234 = 2907 + 532
x + 1234 = 3439
x = 3439 - 1234
x = 2205

a) Ta có: \(2x-2\)\(⋮\)\(x-2\)
\(\Leftrightarrow\)\(2\left(x-2\right)+2\)\(⋮\)\(x-2\)
Ta thấy \(2\left(x-2\right)\)\(⋮\)\(x-2\)
nên \(2\)\(⋮\)\(x-2\)
hay \(x-2\)\(\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)
Ta lập bảng sau:
\(x-2\) \(-2\) \(-1\) \(1\) \(2\)
\(x\) \(0\) \(1\) \(3\) \(4\)
Vậy \(x=\left\{0;1;3;4\right\}\)

\(\dfrac{2x}{15}+\dfrac{2x}{35}+\dfrac{2x}{63}+...+\dfrac{2x}{195}=\dfrac{4}{5}\\ x\cdot\left(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+...+\dfrac{2}{195}\right)=\dfrac{4}{5}\\ x\cdot\left(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+...+\dfrac{2}{13\cdot15}\right)=\dfrac{4}{5}\\ x\cdot\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{13}-\dfrac{1}{15}\right)=\dfrac{4}{5}\\ x\cdot\left(\dfrac{1}{3}-\dfrac{1}{15}\right)=\dfrac{4}{5}\\ x\cdot\dfrac{4}{15}=\dfrac{4}{5}\\ x=\dfrac{4}{5}:\dfrac{4}{15}\\ x=3\)
Gọi \(D=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}\)
\(2D=1-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{16}-\dfrac{1}{32}\\ 2D+D=\left(1-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{16}-\dfrac{1}{32}\right)+\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}\right)\\ 3D=1-\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{16}-\dfrac{1}{32}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}\\ 3D=1-\dfrac{1}{64}< 1\\ \Rightarrow D=\dfrac{1-\dfrac{1}{64}}{3}< \dfrac{1}{3}\)
Vậy \(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}< \dfrac{1}{3}\)
\(\left(2x+1\right).2907=8721\)
\(2x+1=8721:2907\)
\(2x+1=3\)
\(2x=3-1\)
\(2x=2\)
\(x=2:2\)
\(x=1\)
`(2x + 1)‧2907 = 8721`
`2x + 1 = 8721 ÷ 2907`
`2x + 1 = 3`
`2x = 3 - 1`
`2x = 2`
`x = 2÷2`
`x = 1`
Vậy....