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

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

x uchun yechish

$$x=10$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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

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

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

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

3 va 3 ni qisqartiring.

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

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

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

1 ni \frac{2}{2} kasrga o‘giring.

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

-\frac{1}{2} va \frac{2}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

-3 olish uchun -1 dan 2 ni ayirish.

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

\frac{3}{2} ni ikki tarafga qo’shing.

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

6 va 2 ning eng kichik umumiy karralisi 6 ga teng. \frac{1}{6} va \frac{3}{2} ni 6 maxraj bilan kasrlarga aylantirib oling.

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

\frac{1}{6} va \frac{9}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

10 olish uchun 1 va 9'ni qo'shing.

$$\frac{1}{6}x=\frac{10}{6}$$

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

$$\frac{1}{6}x=\frac{5}{3}$$

Ikki tarafini 6 va teskari kasri \frac{1}{6} ga ko‘paytiring.

$$x=\frac{5}{3}\times 6$$

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

$$x=\frac{5\times 6}{3}$$

30 hosil qilish uchun 5 va 6 ni ko'paytirish.

$$x=\frac{30}{3}$$

10 ni olish uchun 30 ni 3 ga bo‘ling.

$$x=10$$