2/3(x-1)=5/6(3-2x)-x eching

$$\frac { 2 } { 3 } ( x - 1 ) = \frac { 5 } { 6 } ( 3 - 2 x ) - x$$

x uchun yechish

$$x=\frac{19}{20}=0,95$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$\frac{2}{3}x+\frac{2}{3}\left(-1\right)=\frac{5}{6}\left(3-2x\right)-x$$

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

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{6}\left(3-2x\right)-x$$

\frac{5}{6} ga 3-2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{6}\times 3+\frac{5}{6}\left(-2\right)x-x$$

\frac{5}{6}\times 3 ni yagona kasrga aylantiring.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5\times 3}{6}+\frac{5}{6}\left(-2\right)x-x$$

15 hosil qilish uchun 5 va 3 ni ko'paytirish.

$$\frac{2}{3}x-\frac{2}{3}=\frac{15}{6}+\frac{5}{6}\left(-2\right)x-x$$

\frac{15}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{2}+\frac{5}{6}\left(-2\right)x-x$$

\frac{5}{6}\left(-2\right) ni yagona kasrga aylantiring.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{2}+\frac{5\left(-2\right)}{6}x-x$$

-10 hosil qilish uchun 5 va -2 ni ko'paytirish.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{2}+\frac{-10}{6}x-x$$

\frac{-10}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

-\frac{8}{3}x ni olish uchun -\frac{5}{3}x va -x ni birlashtirish.

$$\frac{2}{3}x-\frac{2}{3}=\frac{5}{2}-\frac{8}{3}x$$

\frac{8}{3}x ni ikki tarafga qo’shing.

$$\frac{2}{3}x-\frac{2}{3}+\frac{8}{3}x=\frac{5}{2}$$

\frac{10}{3}x ni olish uchun \frac{2}{3}x va \frac{8}{3}x ni birlashtirish.

$$\frac{10}{3}x-\frac{2}{3}=\frac{5}{2}$$

\frac{2}{3} ni ikki tarafga qo’shing.

$$\frac{10}{3}x=\frac{5}{2}+\frac{2}{3}$$

2 va 3 ning eng kichik umumiy karralisi 6 ga teng. \frac{5}{2} va \frac{2}{3} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\frac{10}{3}x=\frac{15}{6}+\frac{4}{6}$$

\frac{15}{6} va \frac{4}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{10}{3}x=\frac{15+4}{6}$$

19 olish uchun 15 va 4'ni qo'shing.

$$\frac{10}{3}x=\frac{19}{6}$$

Ikki tarafini \frac{3}{10} va teskari kasri \frac{10}{3} ga ko‘paytiring.

$$x=\frac{19}{6}\times \frac{3}{10}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{19}{6} ni \frac{3}{10} ga ko‘paytiring.

$$x=\frac{19\times 3}{6\times 10}$$

\frac{19\times 3}{6\times 10} kasridagi ko‘paytirishlarni bajaring.

$$x=\frac{57}{60}$$

\frac{57}{60} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{19}{20}$$