Ta có : \(x-\frac{3}{1.5}-\frac{3}{5.9}-\frac{3}{9.13}-\frac{3}{13.17}-\frac{3}{17.21}=\frac{2}{7}\)

=> \(x-\left(\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+\frac{3}{13.17}+\frac{3}{17.21}\right)=\frac{2}{7}\)

=> \(x-\frac{3}{4}\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+\frac{4}{17.21}\right)=\frac{2}{7}\)

=> \(x-\frac{3}{4}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{3}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}\right)=\frac{2}{7}\)

=> \(x-\frac{3}{4}\left(1-\frac{1}{21}\right)=\frac{2}{7}\)

=> \(x-\frac{3}{4}.\frac{20}{21}=\frac{2}{7}\)

=> \(x-\frac{5}{7}=\frac{2}{7}\)

=> x = 1

Vậy x = 1

Ta có : \(\left(x-\frac{1}{2}\right)^2+\left|y+\frac{1}{3}\right|=0\)

Mà \(\left(x-\frac{1}{2}\right)^2\ge0\forall x\)

       \(\left|x+\frac{1}{3}\right|\ge0\forall x\)

Nên : \(\hept{\begin{cases}\left(x-\frac{1}{2}\right)^2=0\\\left|x+\frac{1}{3}\right|=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x-\frac{1}{2}=0\\x+\frac{1}{3}=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\x=-\frac{1}{3}\end{cases}}\)

c) (x + 9 - 17) - 24 = 11 - (x + 7)

(x + 8) - 24 = 11 - (x + 7)

(x + 8) - 24 = 11 - x - 7

x-8-24=11-x-7

x-8-24=4-x

x -32 = 4 -x 

x + x -32 =4

x + x = 4 +32

2x=36

x=18

a) -5x - 2⁵ = 3x + 2³

    -5x - 32 = 3x + 8

   -5x - 3x - 32 = 8

  -5x - 3x = 8 +32

  -8x = 8+32

  -8x = 40

   x= -5

 b) (26 - x) - (-17 - 2) = -5² - (-13)

26 - x - (-17 - 2) = -5² - (-13)

26 - x - (-19)= -5² - (-13)

26 - x - (-19)= -25 - (-13)

26 - x - (-19)= -25 +13

26 - x +19= -25 +13

26 - x +19= -12

45 -x = -12

-x = -12-45

-x=-57

x=57

1 + 5 + 9 + 13 + 17 +…. + x =507528

Ta có 5 = 2 + 3; 9 = 4 + 5; 13 = 6 + 7; 17 = 8 + 9…

Suy ra x = a (a + 1) (với a ϵ N)

Nên 1 + 5 + 9 + 13 + 17 +…. + x = 1 + 2 + 3 + 4 + 5 + 6 + 7 + ….+ a (a + 1) =507528

Hay ( a + 1) (a + 1 + 1) : 2 = 507528

( a + 1) (a + 2) = 1015056 = 1007. 1008

Suy ra: a = 1006

Do đó: x = 1006 + (1006 + 1) = 2013