a) 5x=-15 <=> x=-3

b) 1-2x=37 <=> 2x=-36 <=> x=-18

c) 2x=-57 <=> x=-57/2

\(\left(6x-16\right).7^8=2.7.7^8\Leftrightarrow6x-16=14\Leftrightarrow6x=30\Leftrightarrow x=5\)

Bài 1

S₂ = 21 + 23 + 25 + ... + 1001

Số số hạng của S₂:

(1001 - 21) : 2 + 1 = 491

⇒ S₂  = (1001 + 21) . 491 : 2 = 250901

--------

S₄  = 15 + 25 + 35 + ... + 115

Số số hạng của S₄:

(115 - 15) : 10 + 1 = 11

⇒ S₄ = (115 + 15) . 11 : 2 = 715

Bài 2

a) 2x - 138 = 2³.3²

2x - 138 = 8.9

2x - 138 = 72

2x = 72 + 138

2x = 210

x = 210 : 2

x = 105

b) 5.(x + 35) = 515

x + 35 = 515 : 5

x + 35 = 103

x = 103 - 35

x = 78

c) 814 - (x - 305) = 712

x - 305 = 814 - 712

x - 305 = 102

x = 102 + 305

x = 407

d) 20 - [7.(x - 3) + 4] = 2

7(x - 3) + 4 = 20 - 2

7(x - 3) + 4 = 18

7(x - 3) = 18 - 4

7(x - 3) = 14

x - 3 = 14 : 7

x - 3 = 2

x = 2 + 3

x = 5

e) 9ˣ⁻¹ = 9

x - 1 = 1

x = 1 + 1

x = 2

2:

a: \(2x-138=2^3\cdot3^2\)

=>\(2x-138=8\cdot9=72\)

=>2x=138+72=210

=>x=105

b: \(5\cdot\left(x+35\right)=515\)

=>x+35=103

=>x=103-35=68

c: \(814-\left(x-305\right)=712\)

=>x-305=814-712=102

=>x=102+305=407

d: \(20-\left[7\left(x-3\right)+4\right]=2\)

=>7(x-3)+4=18

=>7(x-3)=14

=>x-3=2

=>x=5

e: \(9^{x-1}=9\)

=>x-1=1

=>x=2

f: \(5^{x-2}-3^2=2^4-\left(2^8\cdot2^2-2^{10}\cdot2^2\right)\)

=>\(5^{x-2}-9=16-1024+4096\)

=>\(5^{x-2}=3097\)

=>\(x-2=log_53097\)

=>\(x=2+log_53097\)

\(=x^3+2x^2-7x-14-\left(2x^2-28x-x+14\right)+x^3-2x^2-22x+35\)

\(=2x^3-2x^2+7\)

=> |2x - 1| = 11/2

Tìm 2 TH thôi 

7/3 hay sao ấy

ko chắc lắm, mik mới hoc lớp 6 thui à

7/2 : l2x-1l = 21/22

l2x-1l = 7/2 : 21/22 = 7/2 . 22/21 = 11/3

=> 2x-1 = ±11/3

TH1:  2x-1 = -11/3                                              TH2:  2x-1 = 11/3

         2x = -11/3 + 1 = -11/3 + 3/3 = -8/3                       2x = 11/3 + 1 = 11/3 + 3/3 = 14/3

Vậy x\(\in\left\{\frac{-8}{3};\frac{14}{3}\right\}\)

b) Ta có: \(\left(x^2-7\right)\left(x+2\right)-\left(2x-1\right)\left(x-14\right)+x\left(x^2-2x-22\right)+35\)

\(=x^3+2x^2-7x-14-\left(2x^2-28x-x+14\right)+x^3-2x^2-22x+35\)

\(=2x^3-29x+21-2x^2+29x-14\)

\(=2x^3-2x^2+7\)

a: \(542\cdot7+542\cdot2+542\)

\(=542\left(7+2+1\right)\)

\(=542\cdot10=5420\)

b: \(\left(126\cdot35+157\cdot55\right)\cdot\left(132-6\cdot22\right)\)

\(=\left(126\cdot35+157\cdot55\right)\left(132-132\right)\)

\(=0\cdot\left(126\cdot35+157\cdot55\right)\)

=0

c: \(897\cdot99+897\)

\(=897\left(99+1\right)\)

\(=897\cdot100=89700\)

\(\frac{x+4}{y+7}=\frac{4}{7}\Leftrightarrow7\left(x+4\right)=4\left(y+7\right)\)

\(\Leftrightarrow7x+28=4y+28\)

\(\Leftrightarrow7x=4y\Leftrightarrow\frac{x}{4}=\frac{y}{7}\) và x+  y = 22

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{x}{4}=\frac{y}{7}=\frac{x+y}{4+7}=\frac{22}{11}=2\)

+ x = 2 . 4 = 8

+ y = 2 . 7 = 14