Lời giải:

$2^x+2^{x+2}+2^{x+2}=960-2^{x+3}$

$2^x+2^{x+2}+2^{x+2}+2^{x+3}=960$

$2^x(1+2^2+2^2+2^3)=960$

$2^x.17=960$

$2^x=960:17=56,4....$ 

Số khá xấu bạn xem lại nhé.

\(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+99\right)=5450\)

\(\left(x+x+x+...+x\right)+\left(1+2+...+99\right)=5450\)

Từ 1 đến 99 có số số hạng là:

     (99-1):1+1=99 (số hạng)

Tổng các số từ 1 đến 99 là:

     (99+1).99:2=4950

⇒\(\left(x\cdot100\right)+4950=5450\)

⇒\(x\cdot100=5450-4950\)

⇒\(x\cdot100=500\)

⇒\(x=500:100\)

⇒\(x=5\)

Vậy \(x=5\)

x+x+1+x+2+.....+x+99=5450

(x+x+...+x)+(1+2+....+99)=5450

100x+4950=5450

100x=5450-4950

100x=500

      x=500:100

      x=5

vậy x=5

\(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{4}{11\cdot15}+...+\dfrac{4}{198\cdot202}\) (*sửa tí ở phân số đầu tiên nhé !)

\(=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{198}-\dfrac{1}{202}\)

\(=\dfrac{1}{3}+\left(-\dfrac{1}{7}+\dfrac{1}{7}\right)+\left(-\dfrac{1}{11}+\dfrac{1}{11}\right)+...+\left(-\dfrac{1}{198}+\dfrac{1}{198}\right)-\dfrac{1}{202}\)

\(=\dfrac{1}{3}+0+...+0-\dfrac{1}{202}\)

\(=\dfrac{1}{3}-\dfrac{1}{202}\)

\(=\dfrac{199}{606}\)

\(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+...+\dfrac{2}{37\cdot39}\)

\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{37}-\dfrac{1}{39}\) 

\(=\dfrac{1}{3}+\left(-\dfrac{1}{5}+\dfrac{1}{5}\right)+...+\left(-\dfrac{1}{37}+\dfrac{1}{37}\right)-\dfrac{1}{39}\)

\(=\dfrac{1}{3}-\dfrac{1}{39}\)

\(=\dfrac{13}{39}-\dfrac{1}{39}\)

\(=\dfrac{12}{39}\)

\(\dfrac{x-1}{21}=\dfrac{3}{x+1}\)

\(\Rightarrow\left(x-1\right)\left(x+1\right)=3\cdot21\)

\(\Rightarrow x^2+x-x-1=63\)

\(\Rightarrow x^2-1=63\)

\(\Rightarrow x^2=63+1\)

\(\Rightarrow x^2=64\)

\(\Rightarrow x^2=8^2\)

\(\Rightarrow x=\pm8\)

Vậy: ...

x-1/21 = 3/x+1

=> (x-1)(x+1) = 21.3

=> x^2 - x + x - 1 = 63

=> x^2 - 1 = 63

=> x^2 = 64

=> x = ±8

Ta có:
\(3^{2022}=3^2\cdot3^{2020}=9\cdot3^{2020}\)

Mà: \(10>9\)

\(\Rightarrow10\cdot3^{2020}>9\cdot3^{2020}\)

\(\Rightarrow10\cdot3^{2020}>3^{2022}\)

2x + 5 ⋮ x - 1

⇒ 2x - 2 + 7 ⋮ x - 1

⇒ 2(x - 1) + 7 ⋮ x - 1

⇒ 7 ⋮ x - 1

⇒ x - 1 ∈ Ư(7) = {1; -1; 7; -7}

⇒ x ∈ {2; 0; 8; -6}  

Thiếu kết luận là bay mất 0.25 điểm rồi:)

\(6\left(x+11\right)-7\left(2-x\right)=26\)

\(\Rightarrow6x+66-14+7x=26\)

\(\Rightarrow13x+52=26\)

\(\Rightarrow13x=26-52\)

\(\Rightarrow13x=-26\)

\(\Rightarrow x=-26:13\)

\(\Rightarrow x=-2\)