2x-1/2[x-1/2(x-1)]=2/3(x-1) eching

$$2 x - \frac { 1 } { 2 } [ x - \frac { 1 } { 2 } ( x - 1 ) ] = \frac { 2 } { 3 } ( x - 1 )$$

x uchun yechish

$$x=-\frac{5}{13}\approx -0,384615385$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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

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

\frac{1}{2}x ni olish uchun x va -\frac{1}{2}x ni birlashtirish.

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

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

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{1}{2} ni \frac{1}{2} ga ko‘paytiring.

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

\frac{-1}{2\times 2} kasridagi ko‘paytirishlarni bajaring.

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

\frac{-1}{4} kasri manfiy belgini olib tashlash bilan -\frac{1}{4} sifatida qayta yozilishi mumkin.

$$2x-\frac{1}{4}x-\frac{1}{2}\times \frac{1}{2}=\frac{2}{3}\left(x-1\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{1}{2} ni \frac{1}{2} ga ko‘paytiring.

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

\frac{-1}{2\times 2} kasridagi ko‘paytirishlarni bajaring.

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

\frac{-1}{4} kasri manfiy belgini olib tashlash bilan -\frac{1}{4} sifatida qayta yozilishi mumkin.

$$2x-\frac{1}{4}x-\frac{1}{4}=\frac{2}{3}\left(x-1\right)$$

\frac{7}{4}x ni olish uchun 2x va -\frac{1}{4}x ni birlashtirish.

$$\frac{7}{4}x-\frac{1}{4}=\frac{2}{3}\left(x-1\right)$$

\frac{2}{3} ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{7}{4}x-\frac{1}{4}=\frac{2}{3}x+\frac{2}{3}\left(-1\right)$$

-\frac{2}{3} hosil qilish uchun \frac{2}{3} va -1 ni ko'paytirish.

$$\frac{7}{4}x-\frac{1}{4}=\frac{2}{3}x-\frac{2}{3}$$

Ikkala tarafdan \frac{2}{3}x ni ayirish.

$$\frac{7}{4}x-\frac{1}{4}-\frac{2}{3}x=-\frac{2}{3}$$

\frac{13}{12}x ni olish uchun \frac{7}{4}x va -\frac{2}{3}x ni birlashtirish.

$$\frac{13}{12}x-\frac{1}{4}=-\frac{2}{3}$$

\frac{1}{4} ni ikki tarafga qo’shing.

$$\frac{13}{12}x=-\frac{2}{3}+\frac{1}{4}$$

3 va 4 ning eng kichik umumiy karralisi 12 ga teng. -\frac{2}{3} va \frac{1}{4} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$\frac{13}{12}x=-\frac{8}{12}+\frac{3}{12}$$

-\frac{8}{12} va \frac{3}{12} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{13}{12}x=\frac{-8+3}{12}$$

-5 olish uchun -8 va 3'ni qo'shing.

$$\frac{13}{12}x=-\frac{5}{12}$$

Ikki tarafini \frac{12}{13} va teskari kasri \frac{13}{12} ga ko‘paytiring.

$$x=-\frac{5}{12}\times \frac{12}{13}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{5}{12} ni \frac{12}{13} ga ko‘paytiring.

$$x=\frac{-5\times 12}{12\times 13}$$

Surat va maxrajdagi ikkala 12 ni qisqartiring.

$$x=\frac{-5}{13}$$

\frac{-5}{13} kasri manfiy belgini olib tashlash bilan -\frac{5}{13} sifatida qayta yozilishi mumkin.

$$x=-\frac{5}{13}$$