a) \(x-\dfrac{3}{7}=\dfrac{5}{4}\)

\(x=\dfrac{5}{4}+\dfrac{3}{7}\)

\(x=\dfrac{47}{28}\)

b) \(\left(x-\dfrac{3}{5}\right):\dfrac{-1}{3}=0,4\)

\(x-\dfrac{3}{5}=0,4.\dfrac{-1}{3}\)

\(x-\dfrac{3}{5}=-\dfrac{2}{15}\)

\(x=-\dfrac{2}{15}+\dfrac{3}{5}\)

\(x=\dfrac{7}{15}\)

a) x= 5/4+3/7

x= 35/28+12/28

x=47/28

b) x-3/5= -0.4/3

x=-0,4/3+3/5 

x= 2/15+9/15

x= 11/15

Ta có: \(\dfrac{x+4}{2021}+\dfrac{x+3}{2022}=\dfrac{x+2}{2023}+\dfrac{x+1}{2024}\)

=>\(\left(\dfrac{x+4}{2021}+1\right)+\left(\dfrac{x+3}{2022}+1\right)-\left(\dfrac{x+2}{2023}+1\right)-\left(\dfrac{x+1}{2024}+1\right)=0\)

=>\(\dfrac{x+2025}{2021}+\dfrac{x+2025}{2022}-\dfrac{x+2025}{2023}-\dfrac{x+2025}{2024}=0\)

=>x+2025=0

=>x=-2025

Phân tích đa thức thành nhân tử:

16\(x^{2^{ }}\) + 8\(x\) + 1 

P  =(-1)ⁿ.(-1)²ⁿ⁺¹.(-1)ⁿ⁺¹

P = (-1)^n+2n+1+n+1

P = (-1)^{(n+2n+n)+(1+1)}

P = (-1)^(3n+n)+2

P = (-1)⁴ⁿ⁺²

P =(-1)^2.(n+1)

P = [(-1)^2_]n

P  = 1ⁿ

P = 1

`(x+1)/2 = (y+3)/4 = (z+5)/6 = (2x + 2)/4 = (4z + 20)/24`

Áp dụng t/chất dãy tỉ số bằng nhau: 

`=> (x+1)/2 = (y+3)/4 = (z+5)/6 = (2x + 2)/4 = (4z + 20)/24 = (2x + 2 + y + 3 -4z - 20)/(4 + 4 - 24) = (-1 + 2 + 3 - 20)/(-16) = (-16)/(-16) = 1`

`=> {((x+1)/2 = 1 -> x = 1 . 2 - 1 = 1),((y+3)/4 = 1 -> y = 1 .4 - 3 = 1),((z+5)/6 = 1-> z = 1.6-5=1)}`

Vậy ...

Đề yêu cầu gì vậy bạn?

Lời giải:

$|x|\geq 6\Rightarrow x\geq 6$ hoặc $x\leq -6$

Với điều kiện như thế này thì không liệt kê được toàn bộ phần tử của $B$ bạn nhé. 

Lời giải:

$\frac{1}{2}(2^{n+4}+2^n)=17$

$2^{n+4}+2^n=17:\frac{1}{2}$

$2^n(2^4+1)=34$

$2^n.17=34$
$2^n=34:17=2=2^1$

$\Rightarrow n=1$

\(a,\dfrac{5}{4}- \left(\dfrac{1}{2}\right)^2\)

\(=\dfrac{5}{4}-\dfrac{1}{4}\)

\(=1\)

\(b,\dfrac{2}{3}\cdot\dfrac{-3}{2}+\dfrac{-7}{2}\cdot\dfrac{2}{3}\)

\(=\dfrac{2}{3}\cdot\left(\dfrac{-3}{2}+\dfrac{-7}{2}\right)\)

\(=\dfrac{2}{3}\cdot-5\)

\(=-\dfrac{10}{3}\)

\(c,\left(\dfrac{1}{5}+\dfrac{4}{13}\right)+\left(\dfrac{-2}{5}+\dfrac{7}{13}\right)-\left(\dfrac{4}{5}-\dfrac{2}{13}\right)\)

\(=\dfrac{1}{5}+\dfrac{4}{13}-\dfrac{2}{5}+\dfrac{7}{13}-\dfrac{4}{5}+\dfrac{2}{13}\)

\(=\left(\dfrac{1}{5}-\dfrac{2}{5}-\dfrac{4}{5}\right)+\left(\dfrac{4}{13}+\dfrac{7}{13}+\dfrac{2}{13}\right)\)

\(=-1+1\)

`=0`