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

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

y uchun yechish

$$y=-2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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

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

\frac{7}{6}y ni olish uchun \frac{2}{3}y va \frac{1}{2}y ni birlashtirish.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}\left(1-2y\right)-4$$

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

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}+\frac{2}{5}\left(-2\right)y-4$$

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

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}+\frac{2\left(-2\right)}{5}y-4$$

-4 hosil qilish uchun 2 va -2 ni ko'paytirish.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}+\frac{-4}{5}y-4$$

\frac{-4}{5} kasri manfiy belgini olib tashlash bilan -\frac{4}{5} sifatida qayta yozilishi mumkin.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}-\frac{4}{5}y-4$$

4 ni \frac{20}{5} kasrga o‘giring.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2}{5}-\frac{4}{5}y-\frac{20}{5}$$

\frac{2}{5} va \frac{20}{5} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{7}{6}y+\frac{1}{3}=\frac{2-20}{5}-\frac{4}{5}y$$

-18 olish uchun 2 dan 20 ni ayirish.

$$\frac{7}{6}y+\frac{1}{3}=-\frac{18}{5}-\frac{4}{5}y$$

\frac{4}{5}y ni ikki tarafga qo’shing.

$$\frac{7}{6}y+\frac{1}{3}+\frac{4}{5}y=-\frac{18}{5}$$

\frac{59}{30}y ni olish uchun \frac{7}{6}y va \frac{4}{5}y ni birlashtirish.

$$\frac{59}{30}y+\frac{1}{3}=-\frac{18}{5}$$

Ikkala tarafdan \frac{1}{3} ni ayirish.

$$\frac{59}{30}y=-\frac{18}{5}-\frac{1}{3}$$

5 va 3 ning eng kichik umumiy karralisi 15 ga teng. -\frac{18}{5} va \frac{1}{3} ni 15 maxraj bilan kasrlarga aylantirib oling.

$$\frac{59}{30}y=-\frac{54}{15}-\frac{5}{15}$$

-\frac{54}{15} va \frac{5}{15} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{59}{30}y=\frac{-54-5}{15}$$

-59 olish uchun -54 dan 5 ni ayirish.

$$\frac{59}{30}y=-\frac{59}{15}$$

Ikki tarafini \frac{30}{59} va teskari kasri \frac{59}{30} ga ko‘paytiring.

$$y=-\frac{59}{15}\times \frac{30}{59}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{59}{15} ni \frac{30}{59} ga ko‘paytiring.

$$y=\frac{-59\times 30}{15\times 59}$$

\frac{-59\times 30}{15\times 59} kasridagi ko‘paytirishlarni bajaring.

$$y=\frac{-1770}{885}$$

-2 ni olish uchun -1770 ni 885 ga bo‘ling.

$$y=-2$$