`@` `\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`

\(2+\left(x+3\right)=7\)

\(\Rightarrow2+x+3=7\)

\(\Rightarrow x+5=7\)

\(\Rightarrow x=2\)

\(5+\left(3+x\right)=10\)

\(\Rightarrow5+3+x=10\)

\(\Rightarrow x+8=10\)

\(\Rightarrow x=2\)

\(\left(4+x\right)+1=7\)

\(\Rightarrow4+x+1=7\)

\(\Rightarrow x+5=7\)

\(\Rightarrow x=2\)

\(\left(x+5\right)+3=9\)

\(=x+5+3=9\)

\(\Rightarrow x+8=9\)

\(\Rightarrow x=1\)

\(\left(x-1\right)-4=7\)

\(\Rightarrow x-1-4=7\)

\(\Rightarrow x-5=7\)

\(\Rightarrow x=12\)

\(4-\left(6-x\right)=1\)

\(\Rightarrow4-6-x=1\)

\(\Rightarrow-2-x=1\)

\(\Rightarrow x=-3\)

$\textbf{1)}$

$1+3+5+\cdots+101+x=2600$

$1+3+5+\cdots+101=51^2=2601$

$2601+x=2600$

$x=-1.$

$\textbf{2)}$

$2^{3x}+1285=-167+1453$

$2^{3x}+1285=1286$

$2^{3x}=1$

$3x=0$

$x=0.$

\(x:0,16=9:x\)

\(\Rightarrow x^2=0,16.9\)

\(\Rightarrow x^2=1,44\)

\(\Rightarrow x=\pm1,2\)

cảm ơn ạ=3

$\textbf{1)}$

$\left(1+\dfrac13\right)\left(1+\dfrac18\right)\left(1+\dfrac1{15}\right)\left(1+\dfrac1{24}\right)\cdots\left(1+\dfrac1{99}\right)$

$=\dfrac43\cdot\dfrac98\cdot\dfrac{16}{15}\cdot\dfrac{25}{24}\cdots\dfrac{100}{99}$

$=\dfrac21\cdot\dfrac34\cdot\dfrac45\cdot\dfrac56\cdots\dfrac{10}{11}$

$=\dfrac{2\cdot3\cdot4\cdot\cdots\cdot10}{1\cdot4\cdot5\cdot\cdots\cdot11}$

$=\dfrac{2\cdot3}{11}$

$=\dfrac6{11}.$

$\textbf{2)}$

Giả sử giá gạo tháng $2$ là $100$.

Giá gạo tháng $3$ là $100\times120\%=120.$

Giá gạo tháng $4$ là $120\times90\%=108.$

So với tháng $2$: $108-100=8.$

Vậy giá gạo tháng $4$ cao hơn tháng $2$ là $8\%.$

`a)`

`A(x) + B(x) = 2x - 4x^2 + 1 + x^3 - 4x^2 + 5 - 2x`

                  `= x^3 - ( 4x^2 + 4x^2 ) + ( 2x - 2x ) + ( 1+ 5 )`

                  `= x^3 - 8x^2 + 6`

__________________________________________________________

`b)`

    `P(x) + B(x) = A(x)`

`=>P(x) = A(x) - B(x)`

`=>P(x) = 2x - 4x^2 + 1 + x^3 + 4x^2 - 5 + 2x`

`=>P(x) = x^3 + ( -4x^2 + 4x^2 ) + ( 2x + 2x ) + ( 1 - 5 )`

`=>P(x) = x^3 + 4x - 4`

a: \(\dfrac{x}{6}=\dfrac{8}{3}\)

=>\(x=6\cdot\dfrac{8}{3}=\dfrac{6}{3}\cdot8=8\cdot2=16\)

b: \(\dfrac{5}{x}=\dfrac{4}{9}\)

=>\(x=\dfrac{5\cdot9}{4}=\dfrac{45}{4}\)

c: \(\dfrac{x+3}{-4}=\dfrac{5}{20}\)

=>\(x+3=\dfrac{-4\cdot5}{20}=-1\)

=>x=-1-3=-4

d: \(\dfrac{7}{3+4x}=\dfrac{-2}{9}\)

=>\(4x+3=\dfrac{9\cdot7}{-2}=-\dfrac{63}{2}\)

=>\(4x=-\dfrac{63}{2}-3=-\dfrac{69}{2}\)

=>\(x=-\dfrac{69}{8}\)

f: ĐKXĐ: x<>1

\(\dfrac{3}{x-1}=\dfrac{x-1}{27}\)

=>\(\left(x-1\right)^2=3\cdot27=81\)

=>\(\left[{}\begin{matrix}x-1=9\\x-1=-9\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=10\left(nhận\right)\\x=-8\left(nhận\right)\end{matrix}\right.\)

-12(x-5)+7(3-x)=5

=>-12x+60+21-7x=5

=>-19x+81=5

=>-19x=5-81=-76

=>\(x=\frac{-76}{-19}=4\)

e: \(\left(-4156+2021\right)-\left(119+2021-4156\right)\)

\(=-4156+2021-119-2021+4156\)

\(=\left(-4156+4156\right)+\left(2021-2021\right)-119\)

=0+0-119

=-119

g: \(315\cdot75-\left(15\cdot100-315\cdot25\right)\)

\(=315\cdot75-15\cdot100+315\cdot25\)

\(=315\left(75+25\right)-15\cdot100\)

\(=315\cdot100-15\cdot100=300\cdot100=30000\)

h: \(\left(-489\right)\cdot125-\left(125\cdot11-500\cdot25\right)\)

\(=-489\cdot125-125\cdot11+500\cdot25\)

\(=125\left(-489-11\right)+500\cdot25\)

\(=125\cdot\left(-500\right)+500\cdot25\)

\(=500\left(-125+25\right)\)

\(=500\cdot\left(-100\right)=-50000\)

Bài 2:

a: \(-415-3\left(2x-1\right)^2=-490\)

=>\(3\left(2x-1\right)^2+415=490\)

=>\(3\left(2x-1\right)^2=75\)

=>\(\left(2x-1\right)^2=25\)

=>\(\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=-4\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)

Bài a:

\(Theo.tính.chất.dãy.tỷ.số.bằng.nhau.ta.có:\\ \dfrac{x}{3}=\dfrac{y}{2}=\dfrac{z}{6}=\dfrac{x-y-z}{3-2-6}=\dfrac{30}{-5}=-6\\ Vậy:x=-6.3=-18;y=-6.2=-12;z=-6.6=-36\)

Bài b:

Theo t/c dãy tỉ số bằng nhau, ta có:

\(\dfrac{a}{4}=\dfrac{b}{5}=\dfrac{c}{6}=\dfrac{a+b-c}{4+5-6}=\dfrac{15}{3}=5\\ \Rightarrow a=5.4=20;b=5.5=25;c=5.6=30\\ Vậy:a=20;b=25;c=30\)

c: \(\Leftrightarrow x+7=38\)

hay x=31

15-(2x-3)=6                        (x-2).3=3²

⇔   2x-3=9                      ⇔(x-2).3=9

  ⇔  2x=12                      ⇔x-2=3

    ⇔   x=6                         ⇔x=5

(x+7)-25=13                  450:(x-19)=50

⇔x+7=38                       ⇔x-19=9

⇔x=31                             ⇔x=28