1/2(x+1/3)+1/4(2/3x-frac{1}{6})=x eching

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

x uchun yechish

$$x=\frac{3}{8}=0,375$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{2} ni \frac{1}{3} ga ko‘paytiring.

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

\frac{1\times 1}{2\times 3} kasridagi ko‘paytirishlarni bajaring.

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

\frac{1}{4} ga \frac{2}{3}x-\frac{1}{6} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{4} ni \frac{2}{3} ga ko‘paytiring.

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

\frac{1\times 2}{4\times 3} kasridagi ko‘paytirishlarni bajaring.

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

\frac{2}{12} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{4} ni -\frac{1}{6} ga ko‘paytiring.

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

\frac{1\left(-1\right)}{4\times 6} kasridagi ko‘paytirishlarni bajaring.

$$\frac{1}{2}x+\frac{1}{6}+\frac{1}{6}x+\frac{-1}{24}=x$$

\frac{-1}{24} kasri manfiy belgini olib tashlash bilan -\frac{1}{24} sifatida qayta yozilishi mumkin.

$$\frac{1}{2}x+\frac{1}{6}+\frac{1}{6}x-\frac{1}{24}=x$$

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

$$\frac{2}{3}x+\frac{1}{6}-\frac{1}{24}=x$$

6 va 24 ning eng kichik umumiy karralisi 24 ga teng. \frac{1}{6} va \frac{1}{24} ni 24 maxraj bilan kasrlarga aylantirib oling.

$$\frac{2}{3}x+\frac{4}{24}-\frac{1}{24}=x$$

\frac{4}{24} va \frac{1}{24} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2}{3}x+\frac{4-1}{24}=x$$

3 olish uchun 4 dan 1 ni ayirish.

$$\frac{2}{3}x+\frac{3}{24}=x$$

\frac{3}{24} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{2}{3}x+\frac{1}{8}=x$$

Ikkala tarafdan x ni ayirish.

$$\frac{2}{3}x+\frac{1}{8}-x=0$$

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

$$-\frac{1}{3}x+\frac{1}{8}=0$$

Ikkala tarafdan \frac{1}{8} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-\frac{1}{3}x=-\frac{1}{8}$$

Ikki tarafini -3 va teskari kasri -\frac{1}{3} ga ko‘paytiring.

$$x=-\frac{1}{8}\left(-3\right)$$

-\frac{1}{8}\left(-3\right) ni yagona kasrga aylantiring.

$$x=\frac{-\left(-3\right)}{8}$$

3 hosil qilish uchun -1 va -3 ni ko'paytirish.

$$x=\frac{3}{8}$$