x-1/3[x-1/3(x-9)]=1/9(x-4) eching

$$x - \frac { 1 } { 3 } [ x - \frac { 1 } { 3 } ( x - 9 ) ] = \frac { 1 } { 9 } ( x - 4 )$$

x uchun yechish

$$x=\frac{5}{6}\approx 0,833333333$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

-\frac{1}{3} ga x-9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x-\frac{1}{3}\left(x-\frac{1}{3}x-\frac{1}{3}\left(-9\right)\right)=\frac{1}{9}\left(x-4\right)$$

-\frac{1}{3}\left(-9\right) ni yagona kasrga aylantiring.

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+\frac{-\left(-9\right)}{3}\right)=\frac{1}{9}\left(x-4\right)$$

9 hosil qilish uchun -1 va -9 ni ko'paytirish.

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+\frac{9}{3}\right)=\frac{1}{9}\left(x-4\right)$$

3 ni olish uchun 9 ni 3 ga bo‘ling.

$$x-\frac{1}{3}\left(x-\frac{1}{3}x+3\right)=\frac{1}{9}\left(x-4\right)$$

\frac{2}{3}x ni olish uchun x va -\frac{1}{3}x ni birlashtirish.

$$x-\frac{1}{3}\left(\frac{2}{3}x+3\right)=\frac{1}{9}\left(x-4\right)$$

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

$$x-\frac{1}{3}\times \frac{2}{3}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-4\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{1}{3} ni \frac{2}{3} ga ko‘paytiring.

$$x+\frac{-2}{3\times 3}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-4\right)$$

\frac{-2}{3\times 3} kasridagi ko‘paytirishlarni bajaring.

$$x+\frac{-2}{9}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-4\right)$$

\frac{-2}{9} kasri manfiy belgini olib tashlash bilan -\frac{2}{9} sifatida qayta yozilishi mumkin.

$$x-\frac{2}{9}x-\frac{1}{3}\times 3=\frac{1}{9}\left(x-4\right)$$

3 va 3 ni qisqartiring.

$$x-\frac{2}{9}x-1=\frac{1}{9}\left(x-4\right)$$

\frac{7}{9}x ni olish uchun x va -\frac{2}{9}x ni birlashtirish.

$$\frac{7}{9}x-1=\frac{1}{9}\left(x-4\right)$$

\frac{1}{9} ga x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{7}{9}x-1=\frac{1}{9}x+\frac{1}{9}\left(-4\right)$$

\frac{-4}{9} hosil qilish uchun \frac{1}{9} va -4 ni ko'paytirish.

$$\frac{7}{9}x-1=\frac{1}{9}x+\frac{-4}{9}$$

\frac{-4}{9} kasri manfiy belgini olib tashlash bilan -\frac{4}{9} sifatida qayta yozilishi mumkin.

$$\frac{7}{9}x-1=\frac{1}{9}x-\frac{4}{9}$$

Ikkala tarafdan \frac{1}{9}x ni ayirish.

$$\frac{7}{9}x-1-\frac{1}{9}x=-\frac{4}{9}$$

\frac{2}{3}x ni olish uchun \frac{7}{9}x va -\frac{1}{9}x ni birlashtirish.

$$\frac{2}{3}x-1=-\frac{4}{9}$$

1 ni ikki tarafga qo’shing.

$$\frac{2}{3}x=-\frac{4}{9}+1$$

1 ni \frac{9}{9} kasrga o‘giring.

$$\frac{2}{3}x=-\frac{4}{9}+\frac{9}{9}$$

-\frac{4}{9} va \frac{9}{9} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2}{3}x=\frac{-4+9}{9}$$

5 olish uchun -4 va 9'ni qo'shing.

$$\frac{2}{3}x=\frac{5}{9}$$

Ikki tarafini \frac{3}{2} va teskari kasri \frac{2}{3} ga ko‘paytiring.

$$x=\frac{5}{9}\times \frac{3}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{9} ni \frac{3}{2} ga ko‘paytiring.

$$x=\frac{5\times 3}{9\times 2}$$

\frac{5\times 3}{9\times 2} kasridagi ko‘paytirishlarni bajaring.

$$x=\frac{15}{18}$$

\frac{15}{18} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{5}{6}$$