1/5x-[2/3x-(1-x/2+4)]=3/4(1-x) eching

$$\frac { 1 } { 5 } x - [ \frac { 2 } { 3 } x - ( \frac { 1 - x } { 2 } + 4 ) ] = \frac { 3 } { 4 } ( 1 - x )$$

x uchun yechish

$$x = \frac{225}{13} = 17\frac{4}{13} \approx 17,307692308$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 60 ga, 5,3,2,4 ning eng kichik karralisiga ko‘paytiring.

$$12x-60\left(\frac{2}{3}x-\left(\frac{1-x}{2}+4\right)\right)=45\left(1-x\right)$$

\frac{1-x}{2}+4 teskarisini topish uchun har birining teskarisini toping.

$$12x-60\left(\frac{2}{3}x-\frac{1-x}{2}-4\right)=45\left(1-x\right)$$

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

$$12x-60\left(\frac{2}{3}x-\frac{1-x}{2}-4\right)=45-45x$$

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

$$12x-60\left(\frac{2}{3}x-\left(\frac{1}{2}-\frac{1}{2}x\right)-4\right)=45-45x$$

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

$$12x-60\left(\frac{2}{3}x-\frac{1}{2}-\left(-\frac{1}{2}x\right)-4\right)=45-45x$$

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

$$12x-60\left(\frac{2}{3}x-\frac{1}{2}+\frac{1}{2}x-4\right)=45-45x$$

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

$$12x-60\left(\frac{7}{6}x-\frac{1}{2}-4\right)=45-45x$$

4 ni \frac{8}{2} kasrga o‘giring.

$$12x-60\left(\frac{7}{6}x-\frac{1}{2}-\frac{8}{2}\right)=45-45x$$

-\frac{1}{2} va \frac{8}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$12x-60\left(\frac{7}{6}x+\frac{-1-8}{2}\right)=45-45x$$

-9 olish uchun -1 dan 8 ni ayirish.

$$12x-60\left(\frac{7}{6}x-\frac{9}{2}\right)=45-45x$$

-60 ga \frac{7}{6}x-\frac{9}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12x-60\times \frac{7}{6}x-60\left(-\frac{9}{2}\right)=45-45x$$

-60\times \frac{7}{6} ni yagona kasrga aylantiring.

$$12x+\frac{-60\times 7}{6}x-60\left(-\frac{9}{2}\right)=45-45x$$

-420 hosil qilish uchun -60 va 7 ni ko'paytirish.

$$12x+\frac{-420}{6}x-60\left(-\frac{9}{2}\right)=45-45x$$

-70 ni olish uchun -420 ni 6 ga bo‘ling.

$$12x-70x-60\left(-\frac{9}{2}\right)=45-45x$$

-60\left(-\frac{9}{2}\right) ni yagona kasrga aylantiring.

$$12x-70x+\frac{-60\left(-9\right)}{2}=45-45x$$

540 hosil qilish uchun -60 va -9 ni ko'paytirish.

$$12x-70x+\frac{540}{2}=45-45x$$

270 ni olish uchun 540 ni 2 ga bo‘ling.

$$12x-70x+270=45-45x$$

-58x ni olish uchun 12x va -70x ni birlashtirish.

$$-58x+270=45-45x$$

45x ni ikki tarafga qo’shing.

$$-58x+270+45x=45$$

-13x ni olish uchun -58x va 45x ni birlashtirish.

$$-13x+270=45$$

Ikkala tarafdan 270 ni ayirish.

$$-13x=45-270$$

-225 olish uchun 45 dan 270 ni ayirish.

$$-13x=-225$$

Ikki tarafini -13 ga bo‘ling.

$$x=\frac{-225}{-13}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-225}{-13} kasrini \frac{225}{13} ga soddalashtirish mumkin.

$$x=\frac{225}{13}$$