a) 5(2x -1) - 4(8 - 3x) = 7

<=> 10x - 5 - 32 + 12x = 7

<=> 22x = 44 

<=> x =2

Vậy x = 2 là nghiệm phương trình

b) 7(2x - 5) - 5(7x - 2) + 2(5x - 7) = (x - 2) - (x + 4) 

<=> 14x - 35 - 35x + 10 + 10x - 14 = x - 2 - x - 4

<=> -11x - 39 = - 6

<=> -11x = 33

<=> x = -3

Vậy x = -3 là nghiệm phương trình 

\(a,10x-5-32+12x=7\)

\(22x=44\)

\(x=2\)

\(b,14x-35-35x+10+10x-14=x-2-x-4\)

\(-11x-39=-6\)

\(-11x=-33\)

\(x=3\)

a: =>x=3/7+3/5=15/35+21/35=36/35

b: =>x/35=4/5-5/7=28/35-25/35=3/35

=>x=3

c: =>x<3/4+8/4=11/4

=>\(x\in\left\{0;1;2;3\right\}\)

d: =>5/3<x<5/6+24/6=29/6

=>\(x\in\left\{2;3;4\right\}\)

e: =>x<10/12-9/12=1/12

=>x=0

f: =>2/3<x<12/6-5/6=7/6

=>x=1

Bài 3:

a: \(S=1+5^2+5^4+\cdots+5^{200}\)

=>25S=\(5^2+5^4+5^6+\cdots+5^{202}\)

=>25S-S=\(5^2+5^4+\cdots+5^{202}-1-5^2-\cdots-5^{200}\)

=>24S=\(5^{202}-1\)

=>\(S=\frac{5^{202}-1}{24}\)

b: \(4^{30}=\left(2^2\right)^{30}=2^{60}=2^{30}\cdot2^{30}=8^{10}\cdot4^{15}\)

\(3\cdot24^{10}=3\cdot3^{10}\cdot8^{10}=8^{10}\cdot3^{11}\)

mà \(4^{15}>3^{11}\)

nên \(4^{30}>3\cdot24^{10}\)

=>\(2^{30}+3^{30}+4^{30}>3\cdot24^{10}\)

Bài 2:

a: |2x-3|>5

=>\(\left[\begin{array}{l}2x-3>5\\ 2x-3<-5\end{array}\right.\Rightarrow\left[\begin{array}{l}2x>8\\ 2x<-2\end{array}\right.\Rightarrow\left[\begin{array}{l}x>4\\ x<-1\end{array}\right.\)

c: |3x-1|<=7

=>-7<=3x-1<=7

=>-6<=3x<=8

=>\(-2\le x\le\frac83\)

d: \(\left|3x-5\right|+\left|2x+3\right|=7\) (1)

TH1: \(x<-\frac32\)

=>2x+3<0; 3x-5<0

(1) sẽ trở thành: -2x-3-3x+5=7

=>-5x+2=7

=>-5x=5

=>x=-1(loại)

TH2: -3/2<=x<5/3

=>2x+3>=0; 3x-5<0

(1) sẽ trở thành: 2x+3-3x+5=7

=>-x+8=7

=>-x=-1

=>x=-1(nhận)

TH3: x>=5/3

=>2x+3>0; 3x-5>=0

(1) sẽ trở thành: 2x+3+3x-5=7

=>5x-2=7

=>5x=9

=>x=9/5(nhận)

(x-1/2).5/3=7/4-1/2

(x-1/2).5/3=5/4

x-1/2=5/4:5/3

x=3/4+1/2

x=5/4

(x-4/3).7/4=5-7/6

(x+4/3).7/4=23/6

x+4/3=23/6:7/4

x+4/3=46/21

x=46/21-4/3

x=6/7

a, - \(\dfrac{2}{5}\) + \(\dfrac{4}{5}\).\(x\) = \(\dfrac{3}{5}\)

               \(\dfrac{4}{5}\).\(x\) = \(\dfrac{3}{5}\)+ \(\dfrac{2}{5}\)

                 \(\dfrac{4}{5}\).\(x\) = 1

                      \(x\) = \(\dfrac{5}{4}\)

b, - \(\dfrac{3}{7}\) - \(\dfrac{4}{7}\): \(x\) = \(\dfrac{2}{5}\)

              \(\dfrac{4}{7}\): \(x\) = - \(\dfrac{3}{7}\) - \(\dfrac{2}{5}\)

                \(\dfrac{4}{7}\): \(x\) = - \(\dfrac{29}{35}\)

                  \(x\) = \(\dfrac{4}{7}\): (- \(\dfrac{29}{35}\) )

                  \(x\) = - \(\dfrac{20}{29}\)

c, \(\dfrac{4}{7}\).\(x\) + \(\dfrac{2}{3}\) = - \(\dfrac{1}{5}\)

     \(\dfrac{4}{7}\).\(x\)         = -\(\dfrac{1}{5}\) - \(\dfrac{2}{3}\)

      \(\dfrac{4}{7}\).\(x\)       = - \(\dfrac{13}{15}\)

           \(x\)     = - \(\dfrac{13}{15}\): \(\dfrac{4}{7}\)

            \(x\)    = - \(\dfrac{91}{60}\)

a: \(\dfrac{x-3}{5-x}=\dfrac{5}{7}\left(x\ne5\right)\)

=>7(x-3)=5(5-x)

=>7x-21=25-5x

=>12x=46

=>x=23/6

b: \(\dfrac{x-2}{x-1}=\dfrac{x+4}{x+7}\)(ĐKXĐ: \(x\notin\left\{1;-7\right\}\))

=>(x-2)(x+7)=(x+4)(x-1)

=>\(x^2+5x-14=x^2+3x-4\)

=>5x-14=3x-4

=>2x=10

=>x=5(nhận)

Ko chép đề

\(2)x-17+x=x-7\)

\(x+x-x=-7+17\)

\(x=-10\)

Vậy ....

âm 10 , nhỉ ?

Các bạn giúp mình giải với nhé! Đúng thì mình k đúng nhé. Cảm ơn các bạn nhiều lắm. Yêu cả nhà.

\(1.\left(x-5\right)^{23}.\left(y+2\right)^7=0\)

\(\Rightarrow\hept{\begin{cases}\left(x-5\right)^{23}=0\\\left(y+2\right)^7=0\end{cases}\Rightarrow\hept{\begin{cases}\left(x-5\right)^{23}=0^{23}\\\left(y+2\right)^7=0^7\end{cases}}}\)\(\Rightarrow\hept{\begin{cases}x-5=0\\y+2=0\end{cases}\Rightarrow\hept{\begin{cases}x=0+5\\y=0-2\end{cases}}}\)\(\Rightarrow\hept{\begin{cases}x=5\\y=-2\end{cases}}\)

Vậy \(\left(x;y\right)=\left(5;-2\right)\)

1) <=> 8x-16-21-7x=-4

<=> x-37=-4

<=> x=33

2) <=> 12x-48+6x-12-16x-48=-28

<=> 2x-108=-28

<=> 2x = 80

<=> x = 40

3)<=> 4x-20-35+7x+50-10x=-3

<=> x-5=-3

<=> x=2

4) <=> -3x-15=-45-21

<=> 51=3x

<=> 17=x

5) 4x-28+15=-2x+14-10

<=> 6x-13=4

<=> 6x=17

<=> x = \(\frac{17}{6}\)

Chúc bạn học tốt

a) Ta có:

1; 4; 7;...; 100 có (100 - 1) : 3 + 1 = 34 (số)

1 + 4 + 7+ ... + 100 = (100 + 1) × 34 : 2

= 101 × 17

(1 + 4 + 7 + ... + 100) : a = 17

101 × 17 : a = 17

a = 101 × 17 : 17

a = 100

b) (X - 1/2) × 5/3 = 7/4 - 1/2

(X - 1/2) × 5/3 = 5/4

X - 1/2 = 5/4 : 5/3

X - 1/2 = 3/4

X = 3/4 + 1/2

X = 5/4

a) (1 + 4 + 7 +...+ 100) : a = 17

1717 : a = 17

a = 101

b) \(\left(x-\dfrac{1}{2}\right)\times\dfrac{5}{3}=\dfrac{7}{4}-\dfrac{1}{2}\)

\(\left(x-\dfrac{1}{2}\right)\times\dfrac{5}{3}=\dfrac{10}{8}\)

\(\left(x-\dfrac{1}{2}\right)=\dfrac{10}{8}\div\dfrac{5}{3}\)

\(\left(x-\dfrac{1}{2}\right)=\dfrac{10}{8}\times\dfrac{3}{5}\)

\(\left(x-\dfrac{1}{2}\right)=\dfrac{3}{4}\)

\(x-\dfrac{1}{2}=\dfrac{3}{4}\)

\(x=\dfrac{3}{4}+\dfrac{1}{2}\)

\(x=\dfrac{5}{4}\)