1/4x-(2/3x-(1-x/2+1))=3/4(1-x) eching

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

x uchun yechish

$$x = \frac{9}{2} = 4\frac{1}{2} = 4,5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 12 ga, 4,3,2 ning eng kichik karralisiga ko‘paytiring.

$$3x-12\left(\frac{2}{3}x-\left(\frac{1-x}{2}+1\right)\right)=9\left(1-x\right)$$

\frac{1-x}{2}+1 teskarisini topish uchun har birining teskarisini toping.

$$3x-12\left(\frac{2}{3}x-\frac{1-x}{2}-1\right)=9\left(1-x\right)$$

9 ga 1-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x-12\left(\frac{2}{3}x-\frac{1-x}{2}-1\right)=9-9x$$

\frac{1}{2}-\frac{1}{2}x natijani olish uchun 1-x ning har bir ifodasini 2 ga bo‘ling.

$$3x-12\left(\frac{2}{3}x-\left(\frac{1}{2}-\frac{1}{2}x\right)-1\right)=9-9x$$

\frac{1}{2}-\frac{1}{2}x teskarisini topish uchun har birining teskarisini toping.

$$3x-12\left(\frac{2}{3}x-\frac{1}{2}-\left(-\frac{1}{2}x\right)-1\right)=9-9x$$

-\frac{1}{2}x ning teskarisi \frac{1}{2}x ga teng.

$$3x-12\left(\frac{2}{3}x-\frac{1}{2}+\frac{1}{2}x-1\right)=9-9x$$

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

$$3x-12\left(\frac{7}{6}x-\frac{1}{2}-1\right)=9-9x$$

1 ni \frac{2}{2} kasrga o‘giring.

$$3x-12\left(\frac{7}{6}x-\frac{1}{2}-\frac{2}{2}\right)=9-9x$$

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

$$3x-12\left(\frac{7}{6}x+\frac{-1-2}{2}\right)=9-9x$$

-3 olish uchun -1 dan 2 ni ayirish.

$$3x-12\left(\frac{7}{6}x-\frac{3}{2}\right)=9-9x$$

-12 ga \frac{7}{6}x-\frac{3}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x-12\times \frac{7}{6}x-12\left(-\frac{3}{2}\right)=9-9x$$

-12\times \frac{7}{6} ni yagona kasrga aylantiring.

$$3x+\frac{-12\times 7}{6}x-12\left(-\frac{3}{2}\right)=9-9x$$

-84 hosil qilish uchun -12 va 7 ni ko'paytirish.

$$3x+\frac{-84}{6}x-12\left(-\frac{3}{2}\right)=9-9x$$

-14 ni olish uchun -84 ni 6 ga bo‘ling.

$$3x-14x-12\left(-\frac{3}{2}\right)=9-9x$$

-12\left(-\frac{3}{2}\right) ni yagona kasrga aylantiring.

$$3x-14x+\frac{-12\left(-3\right)}{2}=9-9x$$

36 hosil qilish uchun -12 va -3 ni ko'paytirish.

$$3x-14x+\frac{36}{2}=9-9x$$

18 ni olish uchun 36 ni 2 ga bo‘ling.

$$3x-14x+18=9-9x$$

-11x ni olish uchun 3x va -14x ni birlashtirish.

$$-11x+18=9-9x$$

9x ni ikki tarafga qo’shing.

$$-11x+18+9x=9$$

-2x ni olish uchun -11x va 9x ni birlashtirish.

$$-2x+18=9$$

Ikkala tarafdan 18 ni ayirish.

$$-2x=9-18$$

-9 olish uchun 9 dan 18 ni ayirish.

$$-2x=-9$$

Ikki tarafini -2 ga bo‘ling.

$$x=\frac{-9}{-2}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-9}{-2} kasrini \frac{9}{2} ga soddalashtirish mumkin.

$$x=\frac{9}{2}$$