2/3(6-x)-3/4(5-2x)=1/6(3-x) eching

$$\frac { 2 } { 3 } ( 6 - x ) - \frac { 3 } { 4 } ( 5 - 2 x ) = \frac { 1 } { 6 } ( 3 - x )$$

x uchun yechish

$$x=\frac{1}{4}=0,25$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$\frac{2}{3}\times 6+\frac{2}{3}\left(-1\right)x-\frac{3}{4}\left(5-2x\right)=\frac{1}{6}\left(3-x\right)$$

\frac{2}{3}\times 6 ni yagona kasrga aylantiring.

$$\frac{2\times 6}{3}+\frac{2}{3}\left(-1\right)x-\frac{3}{4}\left(5-2x\right)=\frac{1}{6}\left(3-x\right)$$

12 hosil qilish uchun 2 va 6 ni ko'paytirish.

$$\frac{12}{3}+\frac{2}{3}\left(-1\right)x-\frac{3}{4}\left(5-2x\right)=\frac{1}{6}\left(3-x\right)$$

4 ni olish uchun 12 ni 3 ga bo‘ling.

$$4+\frac{2}{3}\left(-1\right)x-\frac{3}{4}\left(5-2x\right)=\frac{1}{6}\left(3-x\right)$$

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

$$4-\frac{2}{3}x-\frac{3}{4}\left(5-2x\right)=\frac{1}{6}\left(3-x\right)$$

-\frac{3}{4} ga 5-2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4-\frac{2}{3}x-\frac{3}{4}\times 5-\frac{3}{4}\left(-2\right)x=\frac{1}{6}\left(3-x\right)$$

-\frac{3}{4}\times 5 ni yagona kasrga aylantiring.

$$4-\frac{2}{3}x+\frac{-3\times 5}{4}-\frac{3}{4}\left(-2\right)x=\frac{1}{6}\left(3-x\right)$$

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

$$4-\frac{2}{3}x+\frac{-15}{4}-\frac{3}{4}\left(-2\right)x=\frac{1}{6}\left(3-x\right)$$

\frac{-15}{4} kasri manfiy belgini olib tashlash bilan -\frac{15}{4} sifatida qayta yozilishi mumkin.

$$4-\frac{2}{3}x-\frac{15}{4}-\frac{3}{4}\left(-2\right)x=\frac{1}{6}\left(3-x\right)$$

-\frac{3}{4}\left(-2\right) ni yagona kasrga aylantiring.

$$4-\frac{2}{3}x-\frac{15}{4}+\frac{-3\left(-2\right)}{4}x=\frac{1}{6}\left(3-x\right)$$

6 hosil qilish uchun -3 va -2 ni ko'paytirish.

$$4-\frac{2}{3}x-\frac{15}{4}+\frac{6}{4}x=\frac{1}{6}\left(3-x\right)$$

\frac{6}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$4-\frac{2}{3}x-\frac{15}{4}+\frac{3}{2}x=\frac{1}{6}\left(3-x\right)$$

4 ni \frac{16}{4} kasrga o‘giring.

$$\frac{16}{4}-\frac{2}{3}x-\frac{15}{4}+\frac{3}{2}x=\frac{1}{6}\left(3-x\right)$$

\frac{16}{4} va \frac{15}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{16-15}{4}-\frac{2}{3}x+\frac{3}{2}x=\frac{1}{6}\left(3-x\right)$$

1 olish uchun 16 dan 15 ni ayirish.

$$\frac{1}{4}-\frac{2}{3}x+\frac{3}{2}x=\frac{1}{6}\left(3-x\right)$$

\frac{5}{6}x ni olish uchun -\frac{2}{3}x va \frac{3}{2}x ni birlashtirish.

$$\frac{1}{4}+\frac{5}{6}x=\frac{1}{6}\left(3-x\right)$$

\frac{1}{6} ga 3-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{4}+\frac{5}{6}x=\frac{1}{6}\times 3+\frac{1}{6}\left(-1\right)x$$

\frac{3}{6} hosil qilish uchun \frac{1}{6} va 3 ni ko'paytirish.

$$\frac{1}{4}+\frac{5}{6}x=\frac{3}{6}+\frac{1}{6}\left(-1\right)x$$

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

$$\frac{1}{4}+\frac{5}{6}x=\frac{1}{2}+\frac{1}{6}\left(-1\right)x$$

-\frac{1}{6} hosil qilish uchun \frac{1}{6} va -1 ni ko'paytirish.

$$\frac{1}{4}+\frac{5}{6}x=\frac{1}{2}-\frac{1}{6}x$$

\frac{1}{6}x ni ikki tarafga qo’shing.

$$\frac{1}{4}+\frac{5}{6}x+\frac{1}{6}x=\frac{1}{2}$$

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

$$\frac{1}{4}+x=\frac{1}{2}$$

Ikkala tarafdan \frac{1}{4} ni ayirish.

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

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

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

\frac{2}{4} va \frac{1}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

1 olish uchun 2 dan 1 ni ayirish.

$$x=\frac{1}{4}$$