a, 5(x+35)=515

(x+35)=103

x=68

b. 96 - 3( x+1) = 42 

<=> 3( x +1 ) = 96 - 42 = 54

<=> x + 1 = 18

<=> x = 17

Ta có : \(\frac{x-1}{99}+\frac{x-3}{97}=\frac{x-4}{96}+\frac{x-6}{94}\)

\(\Leftrightarrow\left(\frac{x-1}{99}-1\right)+\left(\frac{x-3}{97}-1\right)=\left(\frac{x-4}{96}-1\right)+\left(\frac{x-6}{94}-1\right)\)

\(\Leftrightarrow\frac{x-100}{99}+\frac{x-100}{97}=\frac{x-100}{96}+\frac{x-100}{94}\)

\(\Leftrightarrow\frac{x-100}{99}+\frac{x-100}{97}-\frac{x-100}{96}-\frac{x-100}{94}=0\)

\(\Leftrightarrow\left(x-100\right)\left(\frac{1}{99}+\frac{1}{97}-\frac{1}{96}-\frac{1}{94}\right)=0\)

Mà \(\left(\frac{1}{99}+\frac{1}{97}-\frac{1}{96}-\frac{1}{94}\right)\ne0\)

Nên : \(x-100=0\)

Suy ra : \(x=100\)

\(\frac{x-1}{99}+\frac{x-3}{97}=\frac{x-4}{96}+\frac{x-6}{94}\)

\(\Leftrightarrow\frac{x-1}{99}-1+\frac{x-3}{97}-1=\frac{x-4}{96}-1+\frac{x-6}{94}-1\)

\(\Leftrightarrow\frac{x-100}{99}+\frac{x-100}{97}-\frac{x-100}{94}-\frac{x-100}{96}=0\)

\(\Leftrightarrow\left(x-100\right)\left(\frac{1}{99}+\frac{1}{97}-\frac{1}{94}-\frac{1}{96}\right)=0\)

<=>x-100=0

<=>x=100

3.2^x=96

=>x=96:3

=>x=32

=>32=2¹⁶

\(3.2^X=96\Leftrightarrow2^X=96:3=32\)

\(2^X=2^5\Rightarrow X=5\)

use máy tính casio fx 570VN ta đc   x= -100

\(\frac{2}{x}=\frac{3}{y}\)

=> 2y=3x 

=> 2.\(\frac{96}{x}\)= 3x

=> \(\frac{192}{x}=3x\)

=> \(\frac{192}{3}=x^2\)

=> \(x^2=64\)

=> \(\orbr{\begin{cases}x=8\\x=-8\end{cases}}\)

 Với  x=8 thì y =12

Với x= -8 thì y= -12 

Chúc bạn học giỏi

=>x-100=0

=>x=100

\(\dfrac{x+1}{99}+\dfrac{x+2}{98}+\dfrac{x+3}{97}+\dfrac{x+4}{96}=-4\)

\(\Leftrightarrow\dfrac{x+1}{99}+1+\dfrac{x+2}{98}+1+\dfrac{x+3}{97}+1+\dfrac{x+4}{96}+1=0\)

\(\dfrac{x+100}{99}+\dfrac{x+100}{98}+\dfrac{x+100}{97}+\dfrac{x+100}{96}=0\)

\(\Rightarrow x+100=0\Leftrightarrow x=-100\) vậy \(x=-100\)

\(\frac{x-2}{99}+\frac{x-3}{98}=\frac{x-4}{97}+\frac{x-5}{96}\Leftrightarrow\frac{x-2}{99}-1+\frac{x-3}{98}-1=\frac{x-4}{97}-1+\frac{x-5}{96}-1\)

<=>\(\frac{x-101}{99}+\frac{x-101}{98}=\frac{x-101}{97}+\frac{x-101}{96}\)

<=>\(\left(x-101\right)\left(\frac{1}{99}+\frac{1}{98}-\frac{1}{97}-\frac{1}{96}\right)=0\)

<=>x-101=0 \(\left(\frac{1}{99}+\frac{1}{98}-\frac{1}{97}-\frac{1}{96}\ne0\right)\)

<=>x=101

101