\(a,3x-31=-40\Rightarrow3x=-9\Rightarrow x=-3\)

\(b,-3x+37=\left(-4\right)^2\Rightarrow-3x=-21\Rightarrow x=7\)

\(c,\left|2x+7\right|=5\)

\(\Rightarrow\left\{{}\begin{matrix}2x+7=5\Rightarrow x=-1\\2x+7=-5\Rightarrow x=-6\end{matrix}\right.\)

\(d,-x+21=15+2x\Rightarrow3x=6\Rightarrow x=2\)

a) Ta có: 3x-31=-40

\(\Leftrightarrow3x=-9\)

hay x=-3

Vậy: x=-3

b) Ta có: \(-3x+37=\left(-4\right)^2\)

\(\Leftrightarrow-3x+37=16\)

\(\Leftrightarrow-3x=16-37=-21\)

hay x=7

Vậy: x=7

Bạn ơi, bạn viết lại đề đi. Khó nhìn quá

Bài 1: 

a: UCLN(12;52)=4

UC(12;52)={1;2;4}

a: \(x\cdot\dfrac{2}{5}+\dfrac{1}{2}\cdot x=9\)

=>\(x\left(\dfrac{2}{5}+\dfrac{1}{2}\right)=9\)

=>\(x\cdot\dfrac{9}{10}=9\)

=>\(x=9:\dfrac{9}{10}=10\)

b: \(\dfrac{1}{9}:x+\dfrac{3}{9}:x=\dfrac{5}{7}\)

=>\(\left(\dfrac{1}{9}+\dfrac{3}{9}\right):x=\dfrac{5}{7}\)

=>\(\dfrac{4}{9}:x=\dfrac{5}{7}\)

=>\(x=\dfrac{4}{9}:\dfrac{5}{7}=\dfrac{4}{9}\cdot\dfrac{7}{5}=\dfrac{28}{45}\)

Bài 7:

a)(x-15)-75=0

⇔x-15=75

⇔x=90

b)575-(6x+70)=445

⇔6x+70=130

⇔6x=60

⇔x=10

c)x-105:21=15

⇔x-5=15

⇔x=20

d)(x-105):21=15

⇔x-105=315

⇔x=420

a)

\(\begin{array}{l}x - \left( { - \frac{7}{9}} \right) =  - \frac{5}{6}\\x + \frac{7}{9} =  - \frac{5}{6}\\x =  - \frac{5}{6} - \frac{7}{9}\\x =  - \frac{{15}}{{18}} - \frac{{14}}{{18}}\\x = \frac{{ - 29}}{{18}}\end{array}\)

Vậy \(x = \frac{{ - 29}}{{18}}\).

b)

\(\begin{array}{l}\frac{{15}}{{ - 4}} - x = 0,3\\x = \frac{{15}}{{ - 4}} - 0,3\\x =  - 3,75 - 0,3\\x =  - 4,05\end{array}\)

Vậy \(x =  - 4,05\).

2:

a: Gọi d=ƯCLN(4n+7;2n+3)

=>\(\left\{{}\begin{matrix}4n+7⋮d\\2n+3⋮d\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4n+7⋮d\\4n+6⋮d\end{matrix}\right.\Leftrightarrow1⋮d\)

=>d=1

=>ƯCLN(4n+7;2n+3)=1

b: Gọi \(d=ƯCLN\left(3n+5;6n+9\right)\)

=>\(\left\{{}\begin{matrix}3n+5⋮d\\6n+9⋮d\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6n+10⋮d\\6n+9⋮d\end{matrix}\right.\)

=>\(1⋮d\)

=>d=1

=>Đây là phân số tối giản

a)

\(\begin{array}{l}x.\frac{{14}}{{27}} = \frac{{ - 7}}{9}\\x = \frac{{ - 7}}{9}:\frac{{14}}{{27}}\\x = \frac{{ - 7}}{9}.\frac{{27}}{{14}}\\x = \frac{{ - 3}}{2}\end{array}\)                

Vậy \(x = \frac{{ - 3}}{2}\).

b)

\(\begin{array}{l}\left( {\frac{{ - 5}}{9}} \right):x = \frac{2}{3}\\x = \left( {\frac{{ - 5}}{9}} \right):\frac{2}{3}\\x = \left( {\frac{{ - 5}}{9}} \right).\frac{3}{2}\\x = \frac{{ - 5}}{6}\end{array}\)

Vậy \(x = \frac{{ - 5}}{6}\).

c)

\(\begin{array}{l}\frac{2}{5}:x = \frac{1}{{16}}:0,125\\\frac{2}{5}:x = \frac{1}{{16}}:\frac{1}{8}\\\frac{2}{5}:x = \frac{1}{{16}}.8\\\frac{2}{5}:x = \frac{1}{2}\\x = \frac{2}{5}:\frac{1}{2}\\x = \frac{2}{5}.2\\x = \frac{4}{5}\end{array}\)      

Vậy \(x = \frac{4}{5}\)

d)

\(\begin{array}{l} - \frac{5}{{12}}x = \frac{2}{3} - \frac{1}{2}\\ - \frac{5}{{12}}x = \frac{4}{6} - \frac{3}{6}\\ - \frac{5}{{12}}x = \frac{1}{6}\\x = \frac{1}{6}:\left( { - \frac{5}{{12}}} \right)\\x = \frac{1}{6}.\frac{{ - 12}}{5}\\x = \frac{{ - 2}}{5}\end{array}\)

Vậy \(x = \frac{{ - 2}}{5}\).

Chú ý: Khi trình bày lời giải bài tìm x, sau khi tính xong, ta phải kết luận.