a) \(\frac{3}{4}+\frac{1}{4}.x=\frac{1}{2}+\frac{1}{2}x\)

\(\Rightarrow3.\frac{1}{4}+\frac{1}{4}.x=\frac{1}{2}.\left(x+1\right)\)

\(\Rightarrow\frac{1}{4}.\left(x+3\right)=\frac{1}{2}.\left(x+1\right)\)

\(\Rightarrow\frac{x+1}{x+3}=\frac{1}{4}:\frac{1}{2}=\frac{1}{2}\)\(\Rightarrow\left(x+1\right).2=x+3\Rightarrow2x+2=x+3\)

\(\Rightarrow2x-x=3-2\Rightarrow x=1\)

vay x=1

\(\dfrac{5}{6}x-\dfrac{3}{4}=\dfrac{-1}{4}+\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{5}{6}x=\dfrac{7}{6}\)

\(\Rightarrow x=\dfrac{7}{5}\)

b) \(-1\dfrac{1}{2}-\dfrac{2}{3}x=\dfrac{5}{6}-\left(\dfrac{-2}{5}\right)\)

\(\Leftrightarrow\dfrac{2}{3}x=-\dfrac{41}{15}\)

\(\Rightarrow x=-\dfrac{41}{10}\)

c) \(\left(\dfrac{4}{5}:x+1,5\right):\dfrac{2}{3}=-1,5\)

\(\Leftrightarrow\dfrac{8+15x}{10x}.\dfrac{3}{2}=\dfrac{-3}{2}\)

\(\Leftrightarrow\dfrac{24+45x}{20x}=\dfrac{-3}{2}\)

\(\Leftrightarrow-60x=48+90x\)

\(\Rightarrow x=-0,32\)

d) \(\dfrac{4}{3}x-\dfrac{2}{3}=\dfrac{1}{4}-x\)

\(\Leftrightarrow\dfrac{4x-2}{3}=\dfrac{1-4x}{4}\)

\(\Rightarrow16x-8=3-12x\)

\(\Rightarrow x=\dfrac{11}{28}\)

1.b) \(\left(\left|x\right|-3\right)\left(x^2+4\right)< 0\)

\(\Rightarrow\hept{\begin{cases}\left|x\right|-3\\x^2+4\end{cases}}\) trái dấu

\(TH1:\hept{\begin{cases}\left|x\right|-3< 0\\x^2+4>0\end{cases}}\Leftrightarrow\hept{\begin{cases}\left|x\right|< 3\\x^2>-4\end{cases}}\Leftrightarrow x\in\left\{0;\pm1;\pm2\right\}\)

\(TH1:\hept{\begin{cases}\left|x\right|-3>0\\x^2+4< 0\end{cases}}\Leftrightarrow\hept{\begin{cases}\left|x\right|>3\\x^2< -4\end{cases}}\Leftrightarrow x\in\left\{\varnothing\right\}\)

Vậy \(x\in\left\{0;\pm1;\pm2\right\}\)

Bài 1b) có thể giải gọn hơn nhuư thế này

Bài 1:

a) \(\frac{2}{5}+\frac{1}{5}.\left(\frac{3}{4}\right)\)

= \(\frac{2}{5}+\frac{3}{20}\)

= \(\frac{11}{20}\)

b) \(\frac{5}{12}.\left(-\frac{3}{4}\right)\) + \(\frac{7}{12}.\left(-\frac{3}{4}\right)\)

= \(\left(\frac{5}{12}+\frac{7}{12}\right).\left(-\frac{3}{4}\right)\)

= 1.\(\left(-\frac{3}{4}\right)\)

= \(-\frac{3}{4}\)

Còn câu c) đang nghĩ.

Bài 2:

a) \(\frac{5}{7}+\frac{2}{7}\)x = 1

1.x = 1

x = 1 : 1

x = 1

Vậy x = 1.

b) 0,2 + | x - 1, 3 = 1, 5|

0,2 + x = 1, 5 + 1, 3

0,2 + x = 2, 8

x = 2, 8 - 0, 2

x = 2, 6

Vậy x = 2, 6.

c) 2^x + 5 = 37

2^x = 37 - 5

2^x = 32

2^x = 2⁵

=> x = 5

Vậy x = 5.

d) 2^x + 2^{x + 1} = 48

2^x . 1 + 2^x . 2¹ = 48

2^x . ( 1 + 2) = 48

2^x . 3 = 48

2^x = 48 : 3

2^x = 16

2^x = 2⁴

=> x = 4

Vậy x = 4.

Chúc bạn học tốt!

làm bước trung gian giùm mình luôn nhé

thanks trước những bạn làm giùm nhé

mình đang cần gấp lắm sáng mai là mình cần ai đang on làm giùm mình nhé

thanks

a ) \(\left|x-2\right|=2\)

       \(\Rightarrow\orbr{\begin{cases}x-2=2\\x-2=-2\end{cases}}\)

        \(\Rightarrow\orbr{\begin{cases}x=2+2\\x=-2+2\end{cases}}\)

       \(\Rightarrow\orbr{\begin{cases}x=4\\x=0\end{cases}}\) 

Vậy \(x=4\) hoặc \(x=0\)

b ) \(\left|x-\frac{4}{5}\right|=\frac{3}{4}\)

      \(\Rightarrow\orbr{\begin{cases}x-\frac{4}{5}=\frac{3}{4}\\x-\frac{4}{5}=-\frac{3}{4}\end{cases}}\)

       \(\Rightarrow\orbr{\begin{cases}x=\frac{3}{4}+\frac{4}{5}\\x=-\frac{3}{4}+\frac{4}{5}\end{cases}}\)

       \(\Rightarrow\orbr{\begin{cases}x=\frac{15}{20}+\frac{16}{20}\\-\frac{15}{20}+\frac{16}{20}\end{cases}}\)

         \(\Rightarrow\orbr{\begin{cases}x=\frac{31}{20}\\x=\frac{1}{20}\end{cases}}\)

Vậy \(x=\frac{31}{20}\) hoặc \(x=\frac{1}{20}\)

c ) \(6-\left|\frac{1}{2}-x\right|=\frac{2}{5}\)

                 \(\left|\frac{1}{2}-x\right|=6-\frac{2}{5}\)

              \(\left|\frac{1}{2}-x\right|=\frac{28}{5}\)

 \(\Rightarrow\orbr{\begin{cases}\frac{1}{2}-x=\frac{28}{5}\\\frac{1}{2}-x=-\frac{28}{5}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{2}-\frac{28}{5}\\x=\frac{1}{2}-\left(-\frac{28}{5}\right)\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=-\frac{51}{10}\\x=\frac{61}{10}\end{cases}}\)

Vậy \(x=-\frac{51}{10}\) hoặc \(x=\frac{61}{10}\)

d ) \(\frac{1}{5}-\left|\frac{1}{5}.x\right|=\frac{1}{5}\)

                   \(\left|\frac{1}{5}.x\right|=\frac{1}{5}-\frac{1}{5}\)

                    \(\left|\frac{1}{5}.x\right|=0\)

\(\Rightarrow\frac{1}{5}.x=0\)

               \(x=0:\frac{1}{5}\)

                \(x=0\)

Vậy \(x=0\)

e ) \(-2,5+\left|3x+5\right|=-1,5\)

                        \(\left|3x+5\right|=-1,5-\left(-2,5\right)\)

                       \(\left|3x+5\right|=1\)

\(\Rightarrow\orbr{\begin{cases}3x+5=1\\3x+5=-1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}3x=1-5\\3x=-1-5\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}3x=-4\\3x=-6\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=-4:3\\x=-6:3\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=-\frac{4}{3}\\x=-2\end{cases}}\)

Vậy \(x=-\frac{4}{3}\) hoặc \(x=-2\)

g ) \(\left(\frac{2}{3}x-1\right)+\left(\frac{3}{4}x+\frac{1}{2}\right)=0\)

\(\Rightarrow\orbr{\begin{cases}\left(\frac{2}{3}x-1\right)=0\\\left(\frac{3}{4}x+\frac{1}{2}\right)=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}\frac{2}{3}x-1=0\\\frac{3}{4}x+\frac{1}{2}=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}\frac{2}{3}x=0+1\\\frac{3}{4}x=0-\frac{1}{2}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}\frac{2}{3}x=1\\\frac{3}{4}x=-\frac{1}{2}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=1:\frac{2}{3}\\x=-\frac{1}{2}:\frac{3}{4}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=-\frac{2}{3}\end{cases}}\)

Vậy \(x=\frac{3}{2};x=-\frac{2}{3}\)

Bạn bạn hơi dài nhưng đã xong 

Chúc bạn học tốt !!!

Trả lời:

a, | x - 2 | = 2

=> x - 2 = 2 hoặc x - 2 = -2

=>    x = 4                x = 0

Vậy x = 4; x = 0

b, \(\left|x-\frac{4}{5}\right|=\frac{3}{4}\)

\(\Rightarrow x-\frac{4}{5}=\frac{3}{4}\)hoặc \(x-\frac{4}{5}=\frac{-3}{4}\)

\(\Rightarrow x=\frac{31}{20}\)hoặc \(x=\frac{1}{20}\)

Vậy \(x=\frac{31}{20};x=\frac{1}{20}\)

c, \(6-\left|\frac{1}{2}-x\right|=\frac{2}{5}\)

\(\Rightarrow\left|\frac{1}{2}-x\right|=\frac{28}{5}\)

\(\Rightarrow\frac{1}{2}-x=\frac{28}{5}\)hoặc \(\frac{1}{2}-x=\frac{-28}{5}\)

\(\Rightarrow x=\frac{-51}{10}\)hoặc \(x=\frac{61}{10}\)

Vậy \(x=\frac{-51}{10};x=\frac{61}{10}\)

d, \(\frac{1}{5}-\left|\frac{1}{5}\cdot x\right|=\frac{1}{5}\)

\(\Rightarrow\left|\frac{1}{5}\cdot x\right|=0\)

\(\Rightarrow\frac{1}{5}\cdot x=0\)

\(\Rightarrow x=0\)

Vậy x = 0
e, \(-2,5+\left|3x+5\right|=-1,5\)

\(\Rightarrow\left|3x+5\right|=1\)

\(\Rightarrow3x+5=1\)hoặc \(3x+5=-1\)

\(\Rightarrow3x=-4\)hoặc \(3x=-6\)

\(\Rightarrow x=\frac{-4}{3}\)hoặc \(x=-2\)

Vậy \(x=\frac{-4}{3};x=-2\)

g, \(\left(\frac{2}{3}x-1\right)+\left(\frac{3}{4}x+\frac{1}{2}\right)=0\)

\(\Rightarrow\frac{2}{3}x-1+\frac{3}{4}x+\frac{1}{2}=0\)

\(\Rightarrow\frac{17}{12}x-\frac{1}{2}=0\)

\(\Rightarrow\frac{17}{12}x=\frac{1}{2}\)

\(\Rightarrow x=\frac{6}{17}\)

Vậy \(x=\frac{6}{17}\)

a) \(\left|2x-3\right|-\frac{1}{3}=0\)

\(\Leftrightarrow\left|2x-3\right|=\frac{1}{3}\)

\(\Leftrightarrow\orbr{\begin{cases}2x-3=\frac{1}{3}\\2x-3=-\frac{1}{3}\end{cases}}\Leftrightarrow\orbr{\begin{cases}2x=\frac{10}{3}\\2x=\frac{8}{3}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{5}{3}\\x=\frac{4}{3}\end{cases}}\)

b) \(\frac{5}{6}-\left|x+\frac{1}{4}\right|=\frac{1}{4}\)

\(\Leftrightarrow\left|x+\frac{1}{4}\right|=\frac{7}{12}\)

\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{4}=\frac{7}{12}\\x+\frac{1}{4}=-\frac{7}{12}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=-\frac{5}{6}\end{cases}}\)

c) \(3-\left|2x+1,5\right|=\frac{5}{4}\)

\(\Leftrightarrow\left|2x+\frac{3}{2}\right|=\frac{7}{4}\)

\(\Leftrightarrow\orbr{\begin{cases}2x+\frac{3}{2}=\frac{7}{4}\\2x+\frac{3}{2}=-\frac{7}{4}\end{cases}}\Leftrightarrow\orbr{\begin{cases}2x=\frac{1}{4}\\2x=-\frac{13}{4}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{1}{8}\\x=-\frac{13}{8}\end{cases}}\)

a. \(\left|2x-3\right|-\frac{1}{3}=0\)

\(\Leftrightarrow\left|2x-3\right|=\frac{1}{3}\)

\(\Leftrightarrow\orbr{\begin{cases}2x-3=\frac{1}{3}\\2x-3=-\frac{1}{3}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{3}\\x=\frac{4}{3}\end{cases}}\)

b. \(\frac{5}{6}-\left|x+\frac{1}{4}\right|=\frac{1}{4}\)

\(\Leftrightarrow\left|x+\frac{1}{4}\right|=\frac{7}{12}\)

\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{4}=\frac{7}{12}\\x+\frac{1}{4}=-\frac{7}{12}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{1}{3}\\x=-\frac{5}{6}\end{cases}}\)

c. \(3-\left|2x+1,5\right|=\frac{5}{4}\)

\(\Leftrightarrow\left|2x+\frac{3}{2}\right|=\frac{7}{4}\)

\(\Leftrightarrow\orbr{\begin{cases}2x+\frac{3}{2}=\frac{7}{4}\\2x+\frac{3}{2}=-\frac{7}{4}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{8}\\x=-\frac{13}{8}\end{cases}}\)

thích làm mỗi câu d) mấy câu kia nhìn đã ớn rùi mà k thể hiện tư duy

d) = 2^x + 2^x.2 + 2^x.2² + 2^x.2³ =120

       2^x( 1+2+4+8) =120

2^x = 120/15 =8 =2³ 

x =3

a);b) dài lắm ,mk làm c) giúp bn thui, mk còn phải học bài

c) = (1/2)^x + (1/2)^x. (1/2)⁴ = 17

        (1/2)^x(1 + 1/16) =17

(1/2)^x = 1/16 = (1/2)⁴

x  = 4

dễ mà bạn

a) x=4/7 - 1/3=19/21

b) /x-5/=7 -->x-5=7 hoặc x-5=-7

--> x=12 hoặc x= -2