2x-1/9-x-4/5=x eching

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

x uchun yechish

$$x=\frac{31}{44}\approx 0,704545455$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 9 va 5 ning eng kichik umumiy karralisi 45. \frac{2x-1}{9} ni \frac{5}{5} marotabaga ko'paytirish. \frac{x-4}{5} ni \frac{9}{9} marotabaga ko'paytirish.

$$\frac{5\left(2x-1\right)}{45}-\frac{9\left(x-4\right)}{45}=x$$

\frac{5\left(2x-1\right)}{45} va \frac{9\left(x-4\right)}{45} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{5\left(2x-1\right)-9\left(x-4\right)}{45}=x$$

5\left(2x-1\right)-9\left(x-4\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{10x-5-9x+36}{45}=x$$

10x-5-9x+36 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x+31}{45}=x$$

\frac{1}{45}x+\frac{31}{45} natijani olish uchun x+31 ning har bir ifodasini 45 ga bo‘ling.

$$\frac{1}{45}x+\frac{31}{45}=x$$

Ikkala tarafdan x ni ayirish.

$$\frac{1}{45}x+\frac{31}{45}-x=0$$

-\frac{44}{45}x ni olish uchun \frac{1}{45}x va -x ni birlashtirish.

$$-\frac{44}{45}x+\frac{31}{45}=0$$

Ikkala tarafdan \frac{31}{45} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-\frac{44}{45}x=-\frac{31}{45}$$

Ikki tarafini -\frac{45}{44} va teskari kasri -\frac{44}{45} ga ko‘paytiring.

$$x=-\frac{31}{45}\left(-\frac{45}{44}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{31}{45} ni -\frac{45}{44} ga ko‘paytiring.

$$x=\frac{-31\left(-45\right)}{45\times 44}$$

\frac{-31\left(-45\right)}{45\times 44} kasridagi ko‘paytirishlarni bajaring.

$$x=\frac{1395}{1980}$$

\frac{1395}{1980} ulushini 45 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{31}{44}$$