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`@` `\text {Ans}`
`\downarrow`
`2+(x+3)=7`
`\Rightarrow x+3=7-2`
`\Rightarrow x+3=5`
`\Rightarrow x=5-3`
`\Rightarrow x=2`
`5+(3+x)=10`
`\Rightarrow 3+x=10-5`
`\Rightarrow 3+x=5`
`\Rightarrow x=5-3`
`\Rightarrow x=2`
`(4+x)+1=7`
`\Rightarrow 4+x=7-1`
`\Rightarrow 4+x=6`
`\Rightarrow x=6-4`
`\Rightarrow x=2`
`(x+5)+3=9`
`\Rightarrow x+5=9-3`
`\Rightarrow x+5=6`
`\Rightarrow x=6-5`
`\Rightarrow x=1`
`(x-1)-4=7`
`\Rightarrow x-1=7+4`
`\Rightarrow x-1=11`
`\Rightarrow x=11+1`
`\Rightarrow x=12`
`4-(6-x)=1`
`\Rightarrow 6-x=4-1`
`\Rightarrow 6-x=3`
`\Rightarrow x=6-3`
`\Rightarrow x=3`
\(2+\left(x+3\right)=7\)
\(\Rightarrow2+x+3=7\)
\(\Rightarrow x+5=7\)
\(\Rightarrow x=2\)
\(5+\left(3+x\right)=10\)
\(\Rightarrow5+3+x=10\)
\(\Rightarrow x+8=10\)
\(\Rightarrow x=2\)
\(\left(4+x\right)+1=7\)
\(\Rightarrow4+x+1=7\)
\(\Rightarrow x+5=7\)
\(\Rightarrow x=2\)
\(\left(x+5\right)+3=9\)
\(=x+5+3=9\)
\(\Rightarrow x+8=9\)
\(\Rightarrow x=1\)
\(\left(x-1\right)-4=7\)
\(\Rightarrow x-1-4=7\)
\(\Rightarrow x-5=7\)
\(\Rightarrow x=12\)
\(4-\left(6-x\right)=1\)
\(\Rightarrow4-6-x=1\)
\(\Rightarrow-2-x=1\)
\(\Rightarrow x=-3\)

\(\left(x+2\right)-2=0\)
\(\Rightarrow x+2-2=0\)
\(\Rightarrow x=0\)
\(\left(x+3\right)+1=7\)
\(\Rightarrow x+3+1=7\)
\(\Rightarrow x+4=7\)
\(\Rightarrow x=3\)
\(\left(3x-4\right)+4=12\)
\(\Rightarrow3x-4+4=12\)
\(\Rightarrow3x=12\)
\(\Rightarrow x=4\)
\(\left(5x+4\right)-1=13\)
\(\Rightarrow5x+4-1=13\)
\(\Rightarrow5x+3=13\)
\(\Rightarrow5x=10\)
\(\Rightarrow x=2\)
\(\left(4x-8\right)-3=5\)
\(\Rightarrow4x-8-3=5\)
\(\Rightarrow4x-11=5\)
\(\Rightarrow4x=16\)
\(\Rightarrow x=4\)
\(8-\left(2x+4\right)=2\)
\(\Rightarrow8-2x-4=2\)
\(\Rightarrow4-2x=2\)
\(\Rightarrow2x=2\)
\(\Rightarrow x=1\)
\(7+\left(5x+2\right)=14\)
\(\Rightarrow7+5x+2=14\)
\(\Rightarrow9+5x=14\)
\(\Rightarrow5x=5\)
\(\Rightarrow x=1\)
\(5-\left(3x-11\right)=1\)
\(\Rightarrow5-3x+11=1\)
\(\Rightarrow16-3x=1\)
\(\Rightarrow3x=15\)
\(\Rightarrow x=5\)

\(a,TH1:x-2021=0=>x=2021\)
\(Th2:x-2022=0=>x=2022\)
Vậy \(x\in\left\{2021;2022\right\}\)
\(b,x\left(8-5\right)=1080\)
\(x.3=1080\)
\(x=360\)
\(c,x^3=216< =>6^3=216=>x=3\)
\(d,5^5=3125\)
a) ( x- 2021) * ( x- 2022) = 0
=> \(\orbr{\begin{cases}x-2021=0\\x-2022=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2021\\x=2022\end{cases}}}\)
b) b. 8x - 5x = 2022
=> 3x = 2022
=> x = 674
c) \(5\cdot x^3=1080\)
=> \(x^3=216\)
=> \(x^3=6^3\)
=> x = 6
d) \(5^x=3125\)
=> \(5^x=5^5\)
=> x = 5

-5/9 - ( -5/12 ) =-5/9+5/12=-20/36+15/36=-5/36
-1/16 - 1/15=-15/240-16/240=-31/240
11/36 - ( -7/24 )=11/36+7/24=22/72+21/72 =43/72
\(-\frac{5}{9}-\left(-\frac{5}{12}\right)=-\frac{60}{108}-\left(-\frac{45}{108}\right)=-\frac{15}{108}=-\frac{5}{36}.\)
\(\frac{-1}{6}-\frac{1}{15}=\frac{-5}{30}-\frac{2}{30}=\frac{-7}{30}\)
\(\frac{11}{36}-\left(-\frac{7}{24}\right)=\frac{22}{72}-\left(-\frac{21}{72}\right)=\frac{43}{72}\)

1) C = 5 + 52 + 53 + 54 + ... + 520
= (5 + 52) + (53 + 54) + ... +(519 + 520)
= (5 + 52) + 52(5 + 52) + .... + 518(5 + 52)
= (5 + 52)(1 + 52 + ... + 518)
= 26(1 + 52 + ... + 518)
= 13.2.(1 + 52 + ... + 518) \(⋮\)13 (ĐPCM)
2) a) A = 24 + 25 + 26 + 27 + 28 + 29
= (24 + 25) + (26 + 27) + (28 + 29)
= 24(1 + 2) + 26(1 + 2) + 28(1 + 2)
= (1 + 2)(24 + 26 + 28)
= 3(24 + 26 + 28) \(⋮3\)
b) B = 317 + 318 + 319 + 320 + 321 + 322
= (317 + 318 + 319) + (320) + 321 + 322)
= 317(1 + 3 + 32) + 320(1 + 3 + 32)
= (1 + 3 + 32)(317 + 320)
= 13(317 + 320) \(⋮\)13
Bài 1:
C = 5+52 +53+.....+520
=(5+52+53+54)+.....+(517+518+519+520)
=5.(1+5+52+53)+.....+517(1+5+52+53)
=5.156+....+517.156
=156.(5+...+517)=13.12.(5+....+517) chia hết cho 13
Bài 2:
A=24+25+26+27+28+29
=(24+25)+(26+27)+(28+29)
=24(1+2)+26(1+2)+28(1+2)
=24.3+26.3+28.3
=3.(24+26+28) chia hết cho 3
b)
B=317+318+319+320+321+322
=(317+318+319)+(320+321+322)
=317(1+3+32)+320(1+3+32)
=317.13+320.13
=13.(317+320)chia hết cho 13
#CừU


\(\Rightarrow\frac{2x}{4}-\frac{3}{5}=\frac{x}{4}\)
\(\Rightarrow\frac{2x}{4}-\frac{x}{4}=\frac{3}{5}\)
\(\Rightarrow\frac{x}{4}=\frac{3}{5}\)
=> 5x = 12
=> x= 12/5

3(x + 1) + 2(x + 5) = 7
3x + 3 + 2x + 10 = 7
3x + 2x + 3 + 10 = 7
3x + 2x + 13 = 7
x(3 + 2) + 13 = 7
5x + 13 = 7
5x = 7 - 13
5x = -6
x = -6 : 5
x = -1,2
3(x + 1) + 2(x + 5) = 7
3x + 3 + 2x + 10 = 7
3x + 2x + 3 + 10 = 7
3x + 2x + 13 = 7
x(3 + 2) + 13 = 7
5x + 13 = 7
5x = 7 - 13
5x = -6
x = -6 : 5
x = -1,2
Số số hạng của tổng ở vế trái là: \(\frac{x-1}{2}+1=\frac{x+1}{2}\).
\(VT=1+3+5+...+x\). Ta viết lại tổng đó thành:
\(VT=x+x-2+x-4+...+1\)
\(\Rightarrow2VT=\left(1+x\right)+\left(3+x-2\right)+\left(5+x-4\right)+...+\left(x+1\right)\)(có \(\frac{x+1}{2}\)số hạng)
\(2VT=\left(x+1\right)+\left(x+1\right)+\left(x+1\right)+...+\left(x+1\right)\)(có \(\frac{x+1}{2}\)số hạng)
\(2VT=\left(x+1\right).\frac{\left(x+1\right)}{2}=\frac{\left(x+1\right)^2}{2}\)
\(\Rightarrow VT=\frac{\left(x+1\right)^2}{4}\)
Vậy phương trình ban đầu trở thành: \(\frac{\left(x+1\right)^2}{4}=3025\Leftrightarrow\left(x+1\right)^2=12100\Rightarrow x+1=\sqrt{12100}=110\Leftrightarrow x=109\)