a,10

b,6

làm được hai câu thông cảm

dài :vv

a) \(\left|2x-5\right|=4\Leftrightarrow\hept{\begin{cases}2x-5=4\\2x-5=-4\end{cases}\Leftrightarrow\hept{\begin{cases}2x=9\\2x=1\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{9}{2}\\x=\frac{1}{2}\end{cases}}}\)

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

\(\Leftrightarrow\left|\frac{5}{4}-2x\right|=\frac{1}{12}\Leftrightarrow\hept{\begin{cases}\frac{5}{4}-2x=\frac{1}{12}\\\frac{5}{4}-2x=-\frac{1}{12}\end{cases}\Leftrightarrow\hept{\begin{cases}2x=\frac{7}{6}\\2x=\frac{4}{3}\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{7}{12}\\x=\frac{2}{3}\end{cases}}}\)

Bài 1 :

a) \(|2x-5|=4\)

\(\Rightarrow\orbr{\begin{cases}2x-5=4\\2x-5=-4\end{cases}\Rightarrow}\orbr{\begin{cases}2x=9\\2x=1\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{9}{2}\\x=\frac{1}{2}\end{cases}}}\)

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

\(\Rightarrow\left|\frac{5}{4}-2x\right|=\frac{1}{12}\)

\(\Rightarrow\orbr{\begin{cases}\frac{5}{4}-2x=\frac{1}{12}\\\frac{5}{4}-2x=-\frac{1}{12}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}2x=\frac{7}{6}\\2x=\frac{4}{3}\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{7}{12}\\x=\frac{2}{3}\end{cases}}}\)

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

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

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

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

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

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

\(\Rightarrow\left|x+\frac{1}{4}\right|=-\frac{1}{4}\)

Vì \(\left|x\right|\ge0\Rightarrow\)ko có gtri nào của x thỏa mãn đề bài

Bài 2 :

a) \(\left|x-1\right|=3x+2\)

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

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

b|) \(\left|9+x\right|=2x\Rightarrow\orbr{\begin{cases}9+x=2x\\9+x=-2x\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x-2x=-9\\x+2x=-9\end{cases}\Rightarrow\orbr{\begin{cases}-x=-9\\3x=-9\end{cases}\Rightarrow}\orbr{\begin{cases}x=9\\x=-3\end{cases}}}\)

c) \(\left|x+6\right|-9=2x\Rightarrow\left|x+6\right|=2x+9\)

\(\Rightarrow\orbr{\begin{cases}x+6=2x+9\\x+6=-2x-9\end{cases}\Rightarrow}\orbr{\begin{cases}x-2x=9-6\\x+2x=-9-6\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}-x=3\\3x=-15\end{cases}\Rightarrow\orbr{\begin{cases}x=-3\\x=-5\end{cases}}}\)

Cậu có thể tham khảo bài làm trên đây ạ, chúc cậu học tốt ^^

3^x+2=3⁶⁹

=>x+2=69

x=69-2

x=67

2^x-5=8¹⁰

2^x-5=2³⁰

=>x-5=30

x=30+5

x=35

3^x+2+3^x=810

3^x.3²+3^x=810

3^x.(3²+1)=810

3^x.10=810

3^x=810:10

3^x=81

3^x=3⁴

=>x=4

5^x+1-5^x=500

5^x.5-5^x=500

5^x.(5-1)=500

5^x.4=500

5^x=500:4

5^x=125

5^x=5³

=>x=3

a) 3^x+2 = 3⁶⁹

x + 2 = 69

x = 69 - 2

x = 67

b) 2^x-5 = 8¹⁰

2^x-5 = 2³⁰

x  - 5 = 30

x = 30 + 5

x = 35

c) 3^x+2 + 3^x = 810

3^x . 9 + 3^x  . 1 = 810

3^x . ( 9 + 1 ) = 810

3^x . 10 = 810

3^x = 810 : 10

3^x = 81

3^x = 3⁴

=> x = 4

d) 5^x+1 - 5^x = 500

5^x . 5 - 5^x . 1 = 500

5^x . ( 5 - 1 ) = 500

5^x . 4 = 500

5^x = 500 : 4

5^x = 125

5^x = 5³

=> x = 3

a) \(\frac{9}{20}\)                                                   c) \(\frac{-55}{4}\)                                                                                                                                 

b) \(\frac{116}{75}\)                                                d) \(\frac{-76}{45}\)

đúng hết đấy nhé mình tính kĩ lắm ko sai đâu

       chúc may mắn

a) \(\left(4,5-2x\right)\cdot1\frac{4}{7}=\frac{11}{7}\)

\(\left(\frac{9}{2}-2x\right)\cdot\frac{11}{7}=\frac{11}{7}\)

\(\left(\frac{9}{2}-2x\right)=\frac{11}{7}\div\frac{11}{7}\)

\(\left(\frac{9}{2}-2x\right)=1\)

\(2x=\frac{9}{2}-1\)

\(x=\frac{7}{2}\div2\)

\(x=\frac{7}{4}\)

b) \(|\frac{3}{4}\cdot x-\frac{1}{2}|-1=\frac{1}{4}\)

\(|\frac{3}{4}\cdot x-\frac{1}{2}|=\frac{1}{4}+1\)

\(|\frac{3}{4}\cdot x|=\frac{5}{4}+\frac{1}{2}\)

\(x=\frac{7}{4}\div\frac{3}{4}\)

\(x=\frac{7}{3}\)

c) \(\frac{1}{4}-|3-x|=-\frac{3}{4}\)

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

\(|3-x|=1\)

\(x=3-1\)

\(\Rightarrow x=2\)

d) \(4\cdot\left(x-\frac{6}{7}\right)-\frac{3}{5}=1,4\)

\(4\cdot\left(x-\frac{6}{7}\right)-\frac{3}{5}=\frac{7}{5}\)

\(4\cdot\left(x-\frac{6}{7}\right)=\frac{7}{5}+\frac{3}{5}\)

\(4\cdot\left(x-\frac{6}{7}\right)=2\)

\(\left(x-\frac{6}{7}\right)=2\div4\)

\(x=\frac{1}{2}+\frac{6}{7}\)

\(x=\frac{19}{14}\)

\(\)

k cho mình nhé 

chúc bạn học giỏi

|\(\frac32x\) + \(\frac12\)| = |4\(x\) - 1|

\(\left[\begin{array}{l}\frac32x+\frac12=-4x+1\\ \frac32x+\frac12=4x-1\end{array}\right.\)

\(\left[\begin{array}{l}\frac32x+4x=1-\frac12\\ \frac32x-4x=-1-\frac12\end{array}\right.\)

\(\left[\begin{array}{l}\frac{11}{2}x=\frac12\\ -\frac52x=-\frac32\end{array}\right.\)

\(\left[\begin{array}{l}x=\frac12:\frac{11}{2}\\ x=-\frac32:\frac{-5}{2}\end{array}\right.\)

\(\left[\begin{array}{l}x=\frac12\times\frac{2}{11}\\ x=-\frac32\times\frac{-2}{5}\end{array}\right.\)

\(\left[\begin{array}{l}x=\frac{1}{11}\\ x=\frac35\end{array}\right.\)

Vậy \(x\in\) {\(\frac{1}{11};\frac35\)}

|\(\frac54x\) - \(\frac72\)| - |\(\frac58x\) + \(\frac35\)| = 0

|\(\frac54x\) - \(\frac72\)| = |\(\frac58x\) + \(\frac35\)|

\(\left[\begin{array}{l}\frac54x-\frac72=-\frac58x-\frac35\\ \frac54x-\frac72=\frac58x+\frac35\end{array}\right.\)

\(\left[\begin{array}{l}\frac54x+\frac58x=\frac72-\frac35\\ \frac54x-\frac58x=\frac72+\frac35\end{array}\right.\)

\(\left[\begin{array}{l}\frac{15}{8}x=\frac{29}{20}\\ \frac58x=\frac{41}{10}\end{array}\right.\)

\(\left[\begin{array}{l}x=\frac{29}{10}:\frac{15}{8}\\ x=\frac{41}{10}:\frac58\end{array}\right.\)

\(\left[\begin{array}{l}x=\frac{116}{75}\\ x=\frac{164}{25}\end{array}\right.\)

Vậy \(x\in\) {\(\frac{116}{75}\); \(\frac{164}{25}\)}

a) 3*2^x =48 \(\Leftrightarrow\)2^x=16 \(\Leftrightarrow\)x=4                                                                                                                                                                    b) (2^x +1 )³ =5³ \(\Leftrightarrow\)2^x +1 =5 \(\Leftrightarrow\)2^x =4 \(\Leftrightarrow\)x=2                                                                                                                                     c) 36+x=36 \(\Leftrightarrow\)x=0                                                                                                                                                                                          d) 1+x-15=27-1 \(\Leftrightarrow\)x=40

\(4\frac{1}{3}.\left(\frac{1}{6}-\frac{1}{2}\right)\le x\le\frac{2}{3}.\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{4}\right)\)

\(\frac{13}{3}.\frac{-1}{3}\le x\le\frac{2}{3}.\frac{-1}{12}\)

\(\frac{-13}{9}\le x\le\frac{-1}{18}\)

\(\Rightarrow\frac{-26}{18}\le x\le\frac{-1}{18}\)

\(\Rightarrow x\in\left(\frac{-26}{18};...;\frac{-18}{18};...\frac{-1}{18}\right)\)

mà x phải thuộc Z

\(\Rightarrow x=\frac{-18}{18}=-1\)

CHÚC BN HỌC TỐT!