`(x-3)/13+(x-3)/14=(x-3)/15+(x-3)/16`

`=>(x-3).(1/13+1/14-1/15-1/16)=0`

`=>x-3=0` 

`=>x=3`
 

\(\dfrac{x-3}{13}+\dfrac{x-3}{14}=\dfrac{x-3}{15}+\dfrac{x-3}{16}\)

\(\Leftrightarrow\dfrac{x-3}{13}+\dfrac{x-3}{14}-\dfrac{x-3}{15}-\dfrac{x-3}{16}=0\)

\(\Leftrightarrow\left(x-3\right).\left(\dfrac{1}{13}+\dfrac{1}{14}-\dfrac{1}{15}-\dfrac{1}{16}\right)=0\)

\(\Leftrightarrow x-3=0\)( Vì \(\dfrac{1}{13}+\dfrac{1}{14}-\dfrac{1}{15}-\dfrac{1}{16}>0\))

\(\Leftrightarrow x-3=0\Rightarrow x=3\)

a) Ta có: \(\dfrac{2}{3}x-1=\dfrac{3}{2}\)

\(\Leftrightarrow x\cdot\dfrac{2}{3}=\dfrac{5}{2}\)

hay \(x=\dfrac{5}{2}:\dfrac{2}{3}=\dfrac{5}{2}\cdot\dfrac{3}{2}=\dfrac{15}{4}\)

b) Ta có: \(\left|5x-\dfrac{1}{2}\right|-\dfrac{2}{7}=25\%\)

\(\Leftrightarrow\left|5x-\dfrac{1}{2}\right|=\dfrac{1}{4}+\dfrac{2}{7}=\dfrac{15}{28}\)

\(\Leftrightarrow\left[{}\begin{matrix}5x-\dfrac{1}{2}=\dfrac{15}{28}\\5x-\dfrac{1}{2}=\dfrac{-15}{28}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5x=\dfrac{29}{28}\\5x=\dfrac{-1}{28}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{29}{140}\\x=\dfrac{-1}{140}\end{matrix}\right.\)

c) Ta có: \(\dfrac{x-3}{4}=\dfrac{16}{x-3}\)

\(\Leftrightarrow\left(x-3\right)^2=64\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=8\\x-3=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=11\\x=-5\end{matrix}\right.\)

d) Ta có: \(\dfrac{-8}{13}+\dfrac{7}{17}+\dfrac{21}{31}\le x\le\dfrac{-9}{14}+4-\dfrac{5}{14}\)

\(\Leftrightarrow\dfrac{3246}{6851}\le x\le3\)

\(\Leftrightarrow x\in\left\{1;2;3\right\}\)

ko biết =))

Giải:

\(9-3\times\left(x-9\right)=6\) 

      \(3\times\left(x-9\right)=9-6\) 

      \(3\times\left(x-9\right)=3\) 

               \(x-9=3:3\) 

               \(x-9=1\) 

                     \(x=1+9\) 

                     \(x=10\) 

\(4+6\times\left(x+1\right)=70\) 

      \(6\times\left(x+1\right)=70-4\) 

      \(6\times\left(x+1\right)=66\) 

               \(x+1=66:6\) 

               \(x+1=11\) 

                     \(x=11-1\) 

                     \(x=10\) 

\(\dfrac{x}{13}+\dfrac{15}{26}=\dfrac{46}{52}\) 

         \(\dfrac{x}{13}=\dfrac{23}{26}-\dfrac{15}{26}\) 

         \(\dfrac{x}{13}=\dfrac{4}{13}\) 

\(\Rightarrow x=4\) 

\(\dfrac{11}{14}-\dfrac{3}{x}=\dfrac{5}{14}\) 

         \(\dfrac{3}{x}=\dfrac{11}{14}-\dfrac{5}{14}\) 

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

\(\Rightarrow x=7\) 

\(5\times\left(3+7\times x\right)=40\) 

         \(3+7\times x=40:5\) 

         \(3+7\times x=8\) 

                \(7\times x=8-3\) 

                \(7\times x=5\) 

                      \(x=5:7\) 

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

\(x\times6+12:3=120\) 

       \(x\times6+4=120\) 

             \(x\times6=120-4\) 

             \(x\times6=116\) 

                   \(x=116:6\) 

                   \(x=\dfrac{58}{3}\) 

\(x\times3,7+x\times6,3=120\) 

    \(x\times\left(3,7+6,3\right)=120\) 

                  \(x\times10=120\) 

                           \(x=120:10\) 

                           \(x=12\) 

\(\left(15\times24-x\right):0,25=100:\dfrac{1}{4}\) 

      \(\left(360-x\right):0,25=400\) 

                   \(360-x=400.0,25\) 

                   \(360-x=100\) 

                             \(x=360-100\) 

                             \(x=260\) 

\(71+65\times4=\dfrac{x+140}{x}+260\) 

\(\left(x+140\right):x+260=71+260\) 

\(x:x+140:x+260=331\) 

    \(1+140:x+260=331\) 

                    \(140:x=331-1-260\) 

                    \(140:x=70\) 

                             \(x=140:70\) 

                             \(x=2\) 

\(\left(x+1\right)+\left(x+4\right)+\left(x+7\right)+...+\left(x+28\right)=155\) 

                      \(10\times x+\left(1+4+7+...+28\right)=155\)

Số số hạng \(\left(1+4+7+...+28\right)\) :

         \(\left(28-1\right):3+1=10\) 

Tổng dãy \(\left(1+4+7+...+28\right)\) :

         \(\left(1+28\right).10:2=145\) 

\(\Rightarrow10\times x+145=155\) 

               \(10\times x=155-145\) 

               \(10\times x=10\) 

                       \(x=10:10\) 

                       \(x=1\) 

Đều theo cách lớp 5 nha em!

`#3107`

`7/13 \div x = 14/39`

`=> x = 7/13 \div 14/39`

`=> x = 3/2`

Vậy, `x = 3/2`

________

`x \times 3/5 = 14/15`

`=> x = 14/15 \div 3/5`

`=> x = 14/9`

Vậy, `x=14/9.`

\(\dfrac{7}{13}:x=\dfrac{14}{39}\)

\(x=\dfrac{7}{13}:\dfrac{14}{39}\)

\(x=\dfrac{7}{13}\times\dfrac{39}{14}\)

\(x=\dfrac{3}{2}\)

___

\(x\times\dfrac{3}{5}=\dfrac{14}{15}\)

\(x=\dfrac{14}{15}:\dfrac{3}{5}\)

\(x=\dfrac{14}{15}\times\dfrac{5}{3}\)

\(x=\dfrac{14}{9}\)

` 7/13 : x = 14/39 `

`           x = 7/13 : 14/39 `

`           x =  7/13 xx 39/14`

`          x = 3/2`

Vậy ` x=  3/2.`

` x xx 3/5 = 14/15 `

` x = 14/15 : 3/5 `

` x = 14/15 xx 5/3 `

` x = 14/9` 

Vậy ` x = 14/9.`

a)4/5+x=2/3

x=2/3-4/5

x=-2/15

b)-5/6-x=2/3

x=-5/6-2/3

x=-3/2

c)1/2x+3/4=-3/10

1/2x=-3/10-3/4

1/2x=-21/20

x=-21/20:1/2

x=-21/10

d)x/3-1/2=1/5

x/3=1/5+1/2

x/3=7/10

10x/30=21/30

10x=21

x=21:10

x=21/10

câu a) mình chịu (dùng kiến thức lớp 12 chắc làm đc haha)

b) gt ⇒ \(\frac{1}{6}.6^{x+2}-6^x=6^{14}-6^{13}\)

⇒ \(6^{x+1}-6^x=6^{14}-6^{13}\)

⇒ \(6^x\left(6-1\right)=6^{13}\left(6-1\right)\)

⇒ \(x=13\)

c) gt ⇒ \(\frac{1}{2}.2^{x+4}-2^x=2^{13}-2^{10}\)

⇒ \(2^{x+3}-2^x=2^{13}-2^{10}\)

⇒ \(2^x\left(2^3-1\right)=2^{10}\left(2^3-1\right)\)

⇒ \(x=10\)

d) gt ⇒ \(\frac{1}{3}.3^{x+4}-4.3^x=3^{16}-4.3^{13}\)

⇒ \(3^{x+3}-4.3^x=3^{16}-4.3^{13}\)

⇒ \(3^x\left(3^3-4\right)=3^{13}\left(3^3-4\right)\)

⇒ \(x=13\)

câu d chưa có đóng ngoặc kìa bn

Hoàng Tử Hà

Y

Dương Bá Gia Bảo

Nguyễn Thị Diễm Quỳnh

lê thị hương giang

Vũ Huy Hoàng

Nguyễn Thị Linh Chi

Luân Đào

DƯƠNG PHAN KHÁNH DƯƠNG

Nguyễn Ngân Hòa

Nguyễn Huy Tú

Lightning Farron

m.n làm giúp mình với ak

\(\dfrac{x+1}{15}+\dfrac{x+2}{14}=\dfrac{x+3}{13}+\dfrac{x+4}{12}\\ \Rightarrow\left(\dfrac{x+1}{15}+1\right)+\left(\dfrac{x+2}{14}+1\right)-\left(\dfrac{x+3}{13}+1\right)-\left(\dfrac{x+4}{12}+1\right)=0\\ \dfrac{x+16}{15}+\dfrac{x+16}{14}-\dfrac{x+16}{13}-\dfrac{x+16}{12}=0\\ \left(x+16\right)\left(\dfrac{1}{15}+\dfrac{1}{14}-\dfrac{1}{13}-\dfrac{1}{12}\right)=0\\ x+16=0\\ x=-16\)

Ta có: \(\dfrac{x+1}{17}+\dfrac{x+2}{16}=\dfrac{x+3}{15}+\dfrac{x+4}{14}\)

\(\Rightarrow\dfrac{x+1}{17}+1+\dfrac{x+2}{16}+1=\dfrac{x+3}{15}+1+\dfrac{x+4}{14}+1\)

\(\Rightarrow\dfrac{x+18}{17}+\dfrac{x+18}{16}=\dfrac{x+18}{15}+\dfrac{x+18}{14}\)

\(\Rightarrow\dfrac{x+18}{17}+\dfrac{x+18}{16}-\dfrac{x+18}{15}-\dfrac{x+18}{14}=0\)

\(\Rightarrow\left(x+18\right).\left(\dfrac{1}{17}+\dfrac{1}{16}-\dfrac{1}{15}-\dfrac{1}{14}\right)=0\) (1)

Mà \(\dfrac{1}{17}+\dfrac{1}{16}-\dfrac{1}{15}-\dfrac{1}{14}\ne0\) (2)

Từ (1) và (2) => x+18=0 => x=-18

Vậy x=-18

Đăng trùng.

\(\dfrac{15-x}{14}=\dfrac{5}{7}\\ \left(15-x\right)\times7=5\times14\\ \left(15-x\right)\times7=70\\ 15-x=70:7\\ 15-x=10\\ x=15-10\\ x=5\)

__

\(\dfrac{x}{9}=\dfrac{17}{3}\\ x\times3=17\times9\\ x\times3=153\\ x=153:3\\ x=51\)

__

\(15-\dfrac{x}{2}=\dfrac{3}{7}\\ \dfrac{x}{2}=15-\dfrac{3}{7}\\ \dfrac{x}{2}=\dfrac{102}{7}\\ x\times7=102\times2\\ x\times7=204\\ x=204:7\\ x=\dfrac{204}{7}\)

???