1/9[3x-6-5(7x/2-5)]+13(x-5)+1/4=0 eching

$$\frac { 1 } { 9 } [ 3 x - 6 - 5 ( \frac { 7 x } { 2 } - 5 ) ] + 13 ( x - 5 ) + \frac { 1 } { 4 } = 0$$

x uchun yechish

$$x = \frac{11}{2} = 5\frac{1}{2} = 5,5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 36 ga, 9,2,4 ning eng kichik karralisiga ko‘paytiring.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468\left(x-5\right)+9=0$$

468 ga x-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468x-2340+9=0$$

-2331 olish uchun -2340 va 9'ni qo'shing.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468x-2331=0$$

2331 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468x=2331$$

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$8\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+936x=4662$$

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$16\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+1872x=9324$$

-5 ga \frac{7x}{2}-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16\left(3x-6-5\times \frac{7x}{2}+25\right)+1872x=9324$$

-5\times \frac{7x}{2} ni yagona kasrga aylantiring.

$$16\left(3x-6+\frac{-5\times 7x}{2}+25\right)+1872x=9324$$

-35 hosil qilish uchun -5 va 7 ni ko'paytirish.

$$16\left(3x-6+\frac{-35x}{2}+25\right)+1872x=9324$$

19 olish uchun -6 va 25'ni qo'shing.

$$16\left(3x+19+\frac{-35x}{2}\right)+1872x=9324$$

16 ga 3x+19+\frac{-35x}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$48x+304+16\times \frac{-35x}{2}+1872x=9324$$

16 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

$$48x+304+8\left(-35\right)x+1872x=9324$$

-280 hosil qilish uchun 8 va -35 ni ko'paytirish.

$$48x+304-280x+1872x=9324$$

-232x ni olish uchun 48x va -280x ni birlashtirish.

$$-232x+304+1872x=9324$$

1640x ni olish uchun -232x va 1872x ni birlashtirish.

$$1640x+304=9324$$

Ikkala tarafdan 304 ni ayirish.

$$1640x=9324-304$$

9020 olish uchun 9324 dan 304 ni ayirish.

$$1640x=9020$$

Ikki tarafini 1640 ga bo‘ling.

$$x=\frac{9020}{1640}$$

\frac{9020}{1640} ulushini 820 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{11}{2}$$