1/4(3x+5)=1/3(5x-4) eching

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

x uchun yechish

$$x = \frac{31}{11} = 2\frac{9}{11} \approx 2,818181818$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{1}{4} ga 3x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

\frac{3}{4} hosil qilish uchun \frac{1}{4} va 3 ni ko'paytirish.

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

\frac{5}{4} hosil qilish uchun \frac{1}{4} va 5 ni ko'paytirish.

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

\frac{1}{3} ga 5x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

\frac{5}{3} hosil qilish uchun \frac{1}{3} va 5 ni ko'paytirish.

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

\frac{-4}{3} hosil qilish uchun \frac{1}{3} va -4 ni ko'paytirish.

$$\frac{3}{4}x+\frac{5}{4}=\frac{5}{3}x+\frac{-4}{3}$$

\frac{-4}{3} kasri manfiy belgini olib tashlash bilan -\frac{4}{3} sifatida qayta yozilishi mumkin.

$$\frac{3}{4}x+\frac{5}{4}=\frac{5}{3}x-\frac{4}{3}$$

Ikkala tarafdan \frac{5}{3}x ni ayirish.

$$\frac{3}{4}x+\frac{5}{4}-\frac{5}{3}x=-\frac{4}{3}$$

-\frac{11}{12}x ni olish uchun \frac{3}{4}x va -\frac{5}{3}x ni birlashtirish.

$$-\frac{11}{12}x+\frac{5}{4}=-\frac{4}{3}$$

Ikkala tarafdan \frac{5}{4} ni ayirish.

$$-\frac{11}{12}x=-\frac{4}{3}-\frac{5}{4}$$

3 va 4 ning eng kichik umumiy karralisi 12 ga teng. -\frac{4}{3} va \frac{5}{4} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$-\frac{11}{12}x=-\frac{16}{12}-\frac{15}{12}$$

-\frac{16}{12} va \frac{15}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$-\frac{11}{12}x=\frac{-16-15}{12}$$

-31 olish uchun -16 dan 15 ni ayirish.

$$-\frac{11}{12}x=-\frac{31}{12}$$

Ikki tarafini -\frac{12}{11} va teskari kasri -\frac{11}{12} ga ko‘paytiring.

$$x=-\frac{31}{12}\left(-\frac{12}{11}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{31}{12} ni -\frac{12}{11} ga ko‘paytiring.

$$x=\frac{-31\left(-12\right)}{12\times 11}$$

\frac{-31\left(-12\right)}{12\times 11} kasridagi ko‘paytirishlarni bajaring.

$$x=\frac{372}{132}$$

\frac{372}{132} ulushini 12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{31}{11}$$