(1+1/2+1/3)(x-2/frac{1{2}-1/3}+1)=1+2^-1+3^-1 eching

$$( 1 + \frac { 1 } { 2 } + \frac { 1 } { 3 } ) ( \frac { x - 2 } { \frac { 1 } { 2 } - \frac { 1 } { 3 } } + 1 ) = 1 + 2 ^ { - 1 } + 3 ^ { - 1 }$$

x uchun yechish

$$x=2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{3}{2} olish uchun 1 va \frac{1}{2}'ni qo'shing.

$$\left(\frac{3}{2}+\frac{1}{3}\right)\left(\frac{x-2}{\frac{1}{2}-\frac{1}{3}}+1\right)=1+2^{-1}+3^{-1}$$

\frac{11}{6} olish uchun \frac{3}{2} va \frac{1}{3}'ni qo'shing.

$$\frac{11}{6}\left(\frac{x-2}{\frac{1}{2}-\frac{1}{3}}+1\right)=1+2^{-1}+3^{-1}$$

\frac{1}{6} olish uchun \frac{1}{2} dan \frac{1}{3} ni ayirish.

$$\frac{11}{6}\left(\frac{x-2}{\frac{1}{6}}+1\right)=1+2^{-1}+3^{-1}$$

\frac{11}{6} ga \frac{x-2}{\frac{1}{6}}+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=1+2^{-1}+3^{-1}$$

-1 daraja ko‘rsatkichini 2 ga hisoblang va \frac{1}{2} ni qiymatni oling.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=1+\frac{1}{2}+3^{-1}$$

\frac{3}{2} olish uchun 1 va \frac{1}{2}'ni qo'shing.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=\frac{3}{2}+3^{-1}$$

-1 daraja ko‘rsatkichini 3 ga hisoblang va \frac{1}{3} ni qiymatni oling.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=\frac{3}{2}+\frac{1}{3}$$

\frac{11}{6} olish uchun \frac{3}{2} va \frac{1}{3}'ni qo'shing.

$$\frac{11}{6}\times \frac{x-2}{\frac{1}{6}}+\frac{11}{6}=\frac{11}{6}$$

\frac{x}{\frac{1}{6}}+\frac{-2}{\frac{1}{6}} natijani olish uchun x-2 ning har bir ifodasini \frac{1}{6} ga bo‘ling.

$$\frac{11}{6}\left(\frac{x}{\frac{1}{6}}+\frac{-2}{\frac{1}{6}}\right)+\frac{11}{6}=\frac{11}{6}$$

-2 ni \frac{1}{6} ga bo'lish -2 ga k'paytirish \frac{1}{6} ga qaytarish.

$$\frac{11}{6}\left(\frac{x}{\frac{1}{6}}-2\times 6\right)+\frac{11}{6}=\frac{11}{6}$$

-12 hosil qilish uchun -2 va 6 ni ko'paytirish.

$$\frac{11}{6}\left(\frac{x}{\frac{1}{6}}-12\right)+\frac{11}{6}=\frac{11}{6}$$

\frac{11}{6} ga \frac{x}{\frac{1}{6}}-12 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}-22+\frac{11}{6}=\frac{11}{6}$$

-\frac{121}{6} olish uchun -22 va \frac{11}{6}'ni qo'shing.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}-\frac{121}{6}=\frac{11}{6}$$

\frac{121}{6} ni ikki tarafga qo’shing.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}=\frac{11}{6}+\frac{121}{6}$$

22 olish uchun \frac{11}{6} va \frac{121}{6}'ni qo'shing.

$$\frac{11}{6}\times \frac{x}{\frac{1}{6}}=22$$

Ikki tarafini \frac{6}{11} va teskari kasri \frac{11}{6} ga ko‘paytiring.

$$\frac{x}{\frac{1}{6}}=22\times \frac{6}{11}$$

12 hosil qilish uchun 22 va \frac{6}{11} ni ko'paytirish.

$$\frac{x}{\frac{1}{6}}=12$$

Ikkala tarafini \frac{1}{6} ga ko‘paytiring.

$$x=12\times \frac{1}{6}$$

2 hosil qilish uchun 12 va \frac{1}{6} ni ko'paytirish.

$$x=2$$