a: \(x-43=\left(35-x\right)-48\)

=>\(x-43=35-x-48\)

=>\(x-43=-x-13\)

=>\(x+x=-13+43\)

=>2x=30

=>x=30/2=15

b: \(305-x+14=48+\left(x-23\right)\)

=>\(319-x=48+x-23=25+x\)

=>\(x+25=319-x\)

=>\(x+x=319-25\)

=>\(2x=294\)

=>\(x=\dfrac{294}{2}=147\)

c: \(-\left(-x-6+85\right)=\left(x+51\right)-54\)

=>\(-\left(-x+79\right)=x+51-54\)

=>x-79=x-3

=>-79=-3(vô lý)

=>\(x\in\varnothing\)

d: \(-\left(35-x\right)-\left(37-x\right)=33-x\)

=>\(-35+x-37+x=33-x\)

=>2x-72=-x+33

=>\(2x+x=33+72\)

=>3x=105

=>\(x=\dfrac{105}{3}=35\)

Lời giải:

a.

$23+x=15$

$x=15-23=-8$

b.

$x-18=-23$

$x=-23+18=-5$

c.

$x+(-4)=16$

$x=16-(-4)=16+4=20$

d.

$25-x=-16$

$x=25-(-16)=25+16=41$

e.

$(-35)x=-210$

$x=(-210):(-35)=6$
f.

$(-2)(15-x)=60$

$15-x=60:(-2)=-30$
$x=15-(-30)=15+30=45$

a) (71+x)-(-24-x)+(-35-x)=0                                    b)x-34-[(15+x)-(23-x)]=0

     71+x+24+x+-35-x    =0                                      x-34-15-x-23+x       =0

      (x+x-x)+(71+24-35) =0                                     (x-x+x)+(-34-15-23)  =0

              x+60             =0                                              x+-72             =0

              x                   =0-60                                         x                    =0-(-72)

              x                  = -60                                           x                    = 72

a) x = 29

b) x = 1 và x = -5

c) x = 9 và x = -1

\(23+\frac{x}{35}+x=\frac{4}{5}\)

\(\frac{x}{35}+x=\frac{4}{5}-23=-\frac{111}{5}\)

\(\frac{x}{35}+\frac{35x}{35}=-\frac{111}{5}\)

\(\Rightarrow\frac{x\left(35+1\right)}{35}=-\frac{111}{5}\)

\(\Rightarrow\frac{x.36}{35}=-\frac{111}{5}\)

\(\Rightarrow x.36.5=35.\left(-111\right)\)

\(\Rightarrow x.180=-3885\)

\(\Rightarrow x=-3885:180=-\frac{259}{12}\)

Học tốt~~~

a. (5.x + 3) : 4 – 16 = 6

(5.x + 3) : 4  = 22 

(5.x + 3)  = 88 

5.x  = 85

x = 13

b. 7(23 – 3.x) : 2 – 35 = 35

 7(23 – 3.x) : 2 = 70 

7(23 – 3.x) = 35 

 7 . 3.x = 12

7.x = 4 

x = 4/7 

a.) (5.x + 3) : 4 – 16 = 6

=> (5.x + 3) : 4  = 22

=> 5.x + 3  = 88

=>   5x  = 85 

=>   x  =  17

b) 7(23 – 3.x) : 2 – 35 = 35

=>  7(23 – 3.x) : 2  = 70

=>7(23 – 3.x)  = 140

=>   23 – 3.x  =  20

=>    3x    =  3 

=>   x  =  1 

a: \(280-\left(x-140\right):35=270\)

=>(x-140):35=280-270=10

=>x-140=350

=>x=350+140

=>x=490

b: \(\left(190-2x\right):35-32=16\)

=>\(\left(190-2x\right):35=32+16=48\)

=>\(190-2x=35\cdot48=1680\)

=>2x=190-1680=-1490

=>x=-745

c: \(720:\left\lbrack41-\left(2x-5\right)\right\rbrack=2^3\cdot5\)

=>\(720:\left\lbrack41-\left(2x-5\right)\right\rbrack=8\cdot5=40\)

=>41-(2x-5)=720:40=18

=>2x-5=41-18=23

=>2x=28

=>x=14

d: \(\left(x:23+45\right)\cdot37-22=2^4\cdot105\)

=>\(\left(\frac{x}{23}+45\right)\cdot37=16\cdot105+22=1702\)

=>\(\frac{x}{23}+45=46\)

=>\(\frac{x}{23}=1\)

=>x=23

e: \(\left(3x-4\right)\left(x-1\right)^3=0\)

=>\(\left[\begin{array}{l}3x-4=0\\ x-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac43\\ x=1\end{array}\right.\)

f: \(2^{2x-1}:4=8^3\)

=>\(2^{2x-1-2}=2^9\)

=>2x-3=9

=>2x=12

=>x=6

g: \(x^{17}=x\)

=>\(x^{17}-x=0\)

=>\(x\left(x^{16}-1\right)=0\)

=>\(\left[\begin{array}{l}x=0\\ x^{16}-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x^{16}=1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=1\\ x=-1\end{array}\right.\)

h: \(\left(x-5\right)^4=\left(x-5\right)^6\)

=>\(\left(x-5\right)^6-\left(x-5\right)^4=0\)

=>\(\left(x-5\right)^4\cdot\left\lbrack\left(x-5\right)^2-1\right\rbrack=0\)

=>\(\left(x-5\right)^4\cdot\left(x-4\right)\left(x-6\right)=0\)

=>x∈{4;5;6}

i: \(\left(x+2\right)^5=2^{10}\)

=>\(\left(x+2\right)^5=\left(2^2\right)^5=4^5\)

=>x+2=4

=>x=2

k: 1+2+3+...+x=78

=>\(\frac{x\left(x+1\right)}{2}=78\)

=>x(x+1)=156

=>\(x^2+x-156=0\)

=>(x+13)(x-12)=0

=>x=-13(loại) hoặc x=12(nhận)

l: \(\left(3x-2^4\right)\cdot7^3=2\cdot7^4\)

=>\(3x-16=2\cdot\frac{7^4}{7^3}=2\cdot7=14\)

=>3x=16+14=30

=>\(x=\frac{30}{3}=10\)

n: \(5^{x}:5^2=125\)

=>\(5^{x-2}=5^3\)

=>x-2=3

=>x=5

m: \(\left(x+1\right)^2=\left(x+1\right)^0\)

=>\(\left(x+1\right)^2=1\)

=>\(\left[\begin{array}{l}x+1=1\\ x+1=-1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=-2\end{array}\right.\)

o: Số số hạng của dãy số 2;4;..;52 là:

(52-2):2+1=50:2+1=25+1=26(số)

Tổng của dãy số 2;4;...;52 là:

\(\left(52+2\right)\cdot\frac{26}{2}=54\cdot13=702\)

(2+x)+(4+x)+...+(52+x)=780

=>26x+702=780

=>26x=78

=>x=3

p: \(70=2\cdot5\cdot7;80=2^4\cdot5\)

=>ƯCLN(70;80)=\(2\cdot5=10\)

70⋮x; 80⋮x

=>x∈ƯC(70;80)

=>x∈Ư(10)

mà x>8

nên x=10

q: \(12=2^2\cdot3;25=5^2;30=2\cdot3\cdot5\)

=>BCNN(12;25;30)=\(2^2\cdot3\cdot5^2=300\)

x⋮12; x⋮25; x⋮30

=>x∈BC(12;25;30)

=>x∈B(300)

mà 0<x<500

nên x=300

Bài 1:

\(180=2^2\cdot3^2\cdot5\)

Bài 2:

1: \(D=\overline{2x5y}\)

D chia hết cho 2 và 5 nên D chia hết cho 10

=>D có tận cùng là 0

=>y=0

=>\(D=\overline{2x50}\)

D chia hết cho 9

=>2+x+5+0 chia hết cho 9

=>x+7 chia hết cho 9

=>x=2

Vậy: D=2250

2: 

a: \(A=1995+2005+x\)

\(=4000+x\)

A chia hết cho 5

=>\(x+4000⋮5\)

=>\(x⋮5\)

mà \(23< x< 35\)

nên \(x\in\left\{25;30\right\}\)

c: Bạn ghi lại đề đi bạn

Bài 1:

a, 2x + 35 = x - 27

    2x - x = -27 - 35

    x = -62

 b, 2x - 41 = 3x + (-23)

     2x - 3x = -23 + 41

     -x = 18

     x = -18

c, 4 . (x - 3) - 3 . (x - 5) = 45 . (-2) - 34

   4x - 12 - 3x + 15 = -90 - 34

   4x - 3x = -90 - 34 + 12 - 15

   x = -127

Bài 2:

- ( -1234 + 345 - 29 ) - ( 1234 + 135 - 59 )

= 1234 - 345 + 29 - 1234 - 135 + 59

= (1234 - 1234) - (345 + 135) + (29 + 59)

= 0 - 480 + 88

= -392

a)2x+35=x-27

2x-x=-27-35

1x=-62

x=-62:1

X=-62