12(3x/4-x/3)-18(7/9x-5/6x)=x-5 eching

$$12 ( \frac { 3 x } { 4 } - \frac { x } { 3 } ) - 18 ( \frac { 7 } { 9 } x - \frac { 5 } { 6 } x ) = x - 5$$

x uchun yechish

$$x=-1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 36 ga, 4,3,9,6 ning eng kichik karralisiga ko‘paytiring.

$$432\left(\frac{3x}{4}-\frac{x}{3}\right)-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4 va 3 ning eng kichik umumiy karralisi 12. \frac{3x}{4} ni \frac{3}{3} marotabaga ko'paytirish. \frac{x}{3} ni \frac{4}{4} marotabaga ko'paytirish.

$$432\left(\frac{3\times 3x}{12}-\frac{4x}{12}\right)-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

\frac{3\times 3x}{12} va \frac{4x}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$432\times \frac{3\times 3x-4x}{12}-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

3\times 3x-4x ichidagi ko‘paytirishlarni bajaring.

$$432\times \frac{9x-4x}{12}-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

9x-4x kabi iboralarga o‘xshab birlashtiring.

$$432\times \frac{5x}{12}-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

432 va 12 ichida eng katta umumiy 12 faktorini bekor qiling.

$$36\times 5x-648\left(\frac{7}{9}x-\frac{5}{6}x\right)=36x-180$$

-\frac{1}{18}x ni olish uchun \frac{7}{9}x va -\frac{5}{6}x ni birlashtirish.

$$36\times 5x-648\left(-\frac{1}{18}\right)x=36x-180$$

648\left(-\frac{1}{18}\right) ni yagona kasrga aylantiring.

$$36\times 5x-\frac{648\left(-1\right)}{18}x=36x-180$$

-648 hosil qilish uchun 648 va -1 ni ko'paytirish.

$$36\times 5x-\frac{-648}{18}x=36x-180$$

-36 ni olish uchun -648 ni 18 ga bo‘ling.

$$36\times 5x-\left(-36x\right)=36x-180$$

-36x ning teskarisi 36x ga teng.

$$36\times 5x+36x=36x-180$$

180 hosil qilish uchun 36 va 5 ni ko'paytirish.

$$180x+36x=36x-180$$

216x ni olish uchun 180x va 36x ni birlashtirish.

$$216x=36x-180$$

Ikkala tarafdan 36x ni ayirish.

$$216x-36x=-180$$

180x ni olish uchun 216x va -36x ni birlashtirish.

$$180x=-180$$

Ikki tarafini 180 ga bo‘ling.

$$x=\frac{-180}{180}$$

-1 ni olish uchun -180 ni 180 ga bo‘ling.

$$x=-1$$