5x-4/x-1+2/3x-3-2x-7/2x-2=3 eching

$$\frac { 5 x - 4 } { x - 1 } + \frac { 2 } { 3 x - 3 } - \frac { 2 x - 7 } { 2 x - 2 } = 3$$

x uchun yechish

$$x = -\frac{19}{6} = -3\frac{1}{6} \approx -3,166666667$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 6\left(x-1\right) ga, x-1,3x-3,2x-2 ning eng kichik karralisiga ko‘paytiring.

$$6\left(5x-4\right)+2\times 2-3\left(2x-7\right)=18\left(x-1\right)$$

6 ga 5x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$30x-24+2\times 2-3\left(2x-7\right)=18\left(x-1\right)$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$30x-24+4-3\left(2x-7\right)=18\left(x-1\right)$$

-20 olish uchun -24 va 4'ni qo'shing.

$$30x-20-3\left(2x-7\right)=18\left(x-1\right)$$

-3 ga 2x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$30x-20-6x+21=18\left(x-1\right)$$

24x ni olish uchun 30x va -6x ni birlashtirish.

$$24x-20+21=18\left(x-1\right)$$

1 olish uchun -20 va 21'ni qo'shing.

$$24x+1=18\left(x-1\right)$$

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

$$24x+1=18x-18$$

Ikkala tarafdan 18x ni ayirish.

$$24x+1-18x=-18$$

6x ni olish uchun 24x va -18x ni birlashtirish.

$$6x+1=-18$$

Ikkala tarafdan 1 ni ayirish.

$$6x=-18-1$$

-19 olish uchun -18 dan 1 ni ayirish.

$$6x=-19$$

Ikki tarafini 6 ga bo‘ling.

$$x=\frac{-19}{6}$$

\frac{-19}{6} kasri manfiy belgini olib tashlash bilan -\frac{19}{6} sifatida qayta yozilishi mumkin.

$$x=-\frac{19}{6}$$