1/2(x-3)-1/3(x+2)=x eching

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

x uchun yechish

$$x = -\frac{13}{5} = -2\frac{3}{5} = -2,6$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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

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

\frac{-3}{2} kasri manfiy belgini olib tashlash bilan -\frac{3}{2} sifatida qayta yozilishi mumkin.

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

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

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

-\frac{1}{3}\times 2 ni yagona kasrga aylantiring.

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

\frac{-2}{3} kasri manfiy belgini olib tashlash bilan -\frac{2}{3} sifatida qayta yozilishi mumkin.

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

\frac{1}{6}x ni olish uchun \frac{1}{2}x va -\frac{1}{3}x ni birlashtirish.

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

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

$$\frac{1}{6}x-\frac{9}{6}-\frac{4}{6}=x$$

-\frac{9}{6} va \frac{4}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{1}{6}x+\frac{-9-4}{6}=x$$

-13 olish uchun -9 dan 4 ni ayirish.

$$\frac{1}{6}x-\frac{13}{6}=x$$

Ikkala tarafdan x ni ayirish.

$$\frac{1}{6}x-\frac{13}{6}-x=0$$

-\frac{5}{6}x ni olish uchun \frac{1}{6}x va -x ni birlashtirish.

$$-\frac{5}{6}x-\frac{13}{6}=0$$

\frac{13}{6} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$-\frac{5}{6}x=\frac{13}{6}$$

Ikki tarafini -\frac{6}{5} va teskari kasri -\frac{5}{6} ga ko‘paytiring.

$$x=\frac{13}{6}\left(-\frac{6}{5}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{13}{6} ni -\frac{6}{5} ga ko‘paytiring.

$$x=\frac{13\left(-6\right)}{6\times 5}$$

\frac{13\left(-6\right)}{6\times 5} kasridagi ko‘paytirishlarni bajaring.

$$x=\frac{-78}{30}$$

\frac{-78}{30} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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