3/4(y+7)+1/2(3y-5)=9/4(2y-1) eching

$$\frac { 3 } { 4 } ( y + 7 ) + \frac { 1 } { 2 } ( 3 y - 5 ) = \frac { 9 } { 4 } ( 2 y - 1 )$$

y uchun yechish

$$y = \frac{20}{9} = 2\frac{2}{9} \approx 2,222222222$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{3}{4} ga y+7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{4}y+\frac{3}{4}\times 7+\frac{1}{2}\left(3y-5\right)=\frac{9}{4}\left(2y-1\right)$$

\frac{3}{4}\times 7 ni yagona kasrga aylantiring.

$$\frac{3}{4}y+\frac{3\times 7}{4}+\frac{1}{2}\left(3y-5\right)=\frac{9}{4}\left(2y-1\right)$$

21 hosil qilish uchun 3 va 7 ni ko'paytirish.

$$\frac{3}{4}y+\frac{21}{4}+\frac{1}{2}\left(3y-5\right)=\frac{9}{4}\left(2y-1\right)$$

\frac{1}{2} ga 3y-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{4}y+\frac{21}{4}+\frac{1}{2}\times 3y+\frac{1}{2}\left(-5\right)=\frac{9}{4}\left(2y-1\right)$$

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

$$\frac{3}{4}y+\frac{21}{4}+\frac{3}{2}y+\frac{1}{2}\left(-5\right)=\frac{9}{4}\left(2y-1\right)$$

\frac{-5}{2} hosil qilish uchun \frac{1}{2} va -5 ni ko'paytirish.

$$\frac{3}{4}y+\frac{21}{4}+\frac{3}{2}y+\frac{-5}{2}=\frac{9}{4}\left(2y-1\right)$$

\frac{-5}{2} kasri manfiy belgini olib tashlash bilan -\frac{5}{2} sifatida qayta yozilishi mumkin.

$$\frac{3}{4}y+\frac{21}{4}+\frac{3}{2}y-\frac{5}{2}=\frac{9}{4}\left(2y-1\right)$$

\frac{9}{4}y ni olish uchun \frac{3}{4}y va \frac{3}{2}y ni birlashtirish.

$$\frac{9}{4}y+\frac{21}{4}-\frac{5}{2}=\frac{9}{4}\left(2y-1\right)$$

4 va 2 ning eng kichik umumiy karralisi 4 ga teng. \frac{21}{4} va \frac{5}{2} ni 4 maxraj bilan kasrlarga aylantirib oling.

$$\frac{9}{4}y+\frac{21}{4}-\frac{10}{4}=\frac{9}{4}\left(2y-1\right)$$

\frac{21}{4} va \frac{10}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{9}{4}y+\frac{21-10}{4}=\frac{9}{4}\left(2y-1\right)$$

11 olish uchun 21 dan 10 ni ayirish.

$$\frac{9}{4}y+\frac{11}{4}=\frac{9}{4}\left(2y-1\right)$$

\frac{9}{4} ga 2y-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{9}{4}y+\frac{11}{4}=\frac{9}{4}\times 2y+\frac{9}{4}\left(-1\right)$$

\frac{9}{4}\times 2 ni yagona kasrga aylantiring.

$$\frac{9}{4}y+\frac{11}{4}=\frac{9\times 2}{4}y+\frac{9}{4}\left(-1\right)$$

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

$$\frac{9}{4}y+\frac{11}{4}=\frac{18}{4}y+\frac{9}{4}\left(-1\right)$$

\frac{18}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{9}{4}y+\frac{11}{4}=\frac{9}{2}y+\frac{9}{4}\left(-1\right)$$

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

$$\frac{9}{4}y+\frac{11}{4}=\frac{9}{2}y-\frac{9}{4}$$

Ikkala tarafdan \frac{9}{2}y ni ayirish.

$$\frac{9}{4}y+\frac{11}{4}-\frac{9}{2}y=-\frac{9}{4}$$

-\frac{9}{4}y ni olish uchun \frac{9}{4}y va -\frac{9}{2}y ni birlashtirish.

$$-\frac{9}{4}y+\frac{11}{4}=-\frac{9}{4}$$

Ikkala tarafdan \frac{11}{4} ni ayirish.

$$-\frac{9}{4}y=-\frac{9}{4}-\frac{11}{4}$$

-\frac{9}{4} va \frac{11}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$-\frac{9}{4}y=\frac{-9-11}{4}$$

-20 olish uchun -9 dan 11 ni ayirish.

$$-\frac{9}{4}y=\frac{-20}{4}$$

-5 ni olish uchun -20 ni 4 ga bo‘ling.

$$-\frac{9}{4}y=-5$$

Ikki tarafini -\frac{4}{9} va teskari kasri -\frac{9}{4} ga ko‘paytiring.

$$y=-5\left(-\frac{4}{9}\right)$$

-5\left(-\frac{4}{9}\right) ni yagona kasrga aylantiring.

$$y=\frac{-5\left(-4\right)}{9}$$

20 hosil qilish uchun -5 va -4 ni ko'paytirish.

$$y=\frac{20}{9}$$