{2/7x+9/2-[(4-5x/7-3x+4/2)-frac{9}{14}x]}-1=frac{3}{2}x eching

$$\{ \frac { 2 } { 7 } x + \frac { 9 } { 2 } - [ ( \frac { 4 - 5 x } { 7 } - \frac { 3 x + 4 } { 2 } ) - \frac { 9 } { 14 } x ] \} - 1 = \frac { 3 } { 2 } x$$

x uchun yechish

$$x=-3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 14 ga, 7,2,14 ning eng kichik karralisiga ko‘paytiring.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{4-5x}{7}-\frac{3x+4}{2}-\frac{9}{14}x\right)\right)-14=21x$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 7 va 2 ning eng kichik umumiy karralisi 14. \frac{4-5x}{7} ni \frac{2}{2} marotabaga ko'paytirish. \frac{3x+4}{2} ni \frac{7}{7} marotabaga ko'paytirish.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{2\left(4-5x\right)}{14}-\frac{7\left(3x+4\right)}{14}-\frac{9}{14}x\right)\right)-14=21x$$

\frac{2\left(4-5x\right)}{14} va \frac{7\left(3x+4\right)}{14} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{2\left(4-5x\right)-7\left(3x+4\right)}{14}-\frac{9}{14}x\right)\right)-14=21x$$

2\left(4-5x\right)-7\left(3x+4\right) ichidagi ko‘paytirishlarni bajaring.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{8-10x-21x-28}{14}-\frac{9}{14}x\right)\right)-14=21x$$

8-10x-21x-28 kabi iboralarga o‘xshab birlashtiring.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\left(\frac{-20-31x}{14}-\frac{9}{14}x\right)\right)-14=21x$$

\frac{-20-31x}{14}-\frac{9}{14}x teskarisini topish uchun har birining teskarisini toping.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\frac{-20-31x}{14}-\left(-\frac{9}{14}x\right)\right)-14=21x$$

-\frac{9}{14}x ning teskarisi \frac{9}{14}x ga teng.

$$14\left(\frac{2}{7}x+\frac{9}{2}-\frac{-20-31x}{14}+\frac{9}{14}x\right)-14=21x$$

\frac{13}{14}x ni olish uchun \frac{2}{7}x va \frac{9}{14}x ni birlashtirish.

$$14\left(\frac{13}{14}x+\frac{9}{2}-\frac{-20-31x}{14}\right)-14=21x$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 va 14 ning eng kichik umumiy karralisi 14. \frac{9}{2} ni \frac{7}{7} marotabaga ko'paytirish.

$$14\left(\frac{13}{14}x+\frac{9\times 7}{14}-\frac{-20-31x}{14}\right)-14=21x$$

\frac{9\times 7}{14} va \frac{-20-31x}{14} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$14\left(\frac{13}{14}x+\frac{9\times 7-\left(-20-31x\right)}{14}\right)-14=21x$$

9\times 7-\left(-20-31x\right) ichidagi ko‘paytirishlarni bajaring.

$$14\left(\frac{13}{14}x+\frac{63+20+31x}{14}\right)-14=21x$$

63+20+31x kabi iboralarga o‘xshab birlashtiring.

$$14\left(\frac{13}{14}x+\frac{83+31x}{14}\right)-14=21x$$

14 ga \frac{13}{14}x+\frac{83+31x}{14} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$14\times \frac{13}{14}x+14\times \frac{83+31x}{14}-14=21x$$

14 va 14 ni qisqartiring.

$$13x+14\times \frac{83+31x}{14}-14=21x$$

14\times \frac{83+31x}{14} ni yagona kasrga aylantiring.

$$13x+\frac{14\left(83+31x\right)}{14}-14=21x$$

14 va 14 ni qisqartiring.

$$13x+83+31x-14=21x$$

44x ni olish uchun 13x va 31x ni birlashtirish.

$$44x+83-14=21x$$

69 olish uchun 83 dan 14 ni ayirish.

$$44x+69=21x$$

Ikkala tarafdan 21x ni ayirish.

$$44x+69-21x=0$$

23x ni olish uchun 44x va -21x ni birlashtirish.

$$23x+69=0$$

Ikkala tarafdan 69 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$23x=-69$$

Ikki tarafini 23 ga bo‘ling.

$$x=\frac{-69}{23}$$

-3 ni olish uchun -69 ni 23 ga bo‘ling.

$$x=-3$$