3(x-5)+3x+1=2(x-2)+15(x-3) eching

$$3 ( x - 5 ) + 3 x + 1 = 2 ( x - 2 ) + 15 ( x - 3 )$$

x uchun yechish

$$x = \frac{35}{11} = 3\frac{2}{11} \approx 3,181818182$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$3x-15+3x+1=2\left(x-2\right)+15\left(x-3\right)$$

6x ni olish uchun 3x va 3x ni birlashtirish.

$$6x-15+1=2\left(x-2\right)+15\left(x-3\right)$$

-14 olish uchun -15 va 1'ni qo'shing.

$$6x-14=2\left(x-2\right)+15\left(x-3\right)$$

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

$$6x-14=2x-4+15\left(x-3\right)$$

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

$$6x-14=2x-4+15x-45$$

17x ni olish uchun 2x va 15x ni birlashtirish.

$$6x-14=17x-4-45$$

-49 olish uchun -4 dan 45 ni ayirish.

$$6x-14=17x-49$$

Ikkala tarafdan 17x ni ayirish.

$$6x-14-17x=-49$$

-11x ni olish uchun 6x va -17x ni birlashtirish.

$$-11x-14=-49$$

14 ni ikki tarafga qo’shing.

$$-11x=-49+14$$

-35 olish uchun -49 va 14'ni qo'shing.

$$-11x=-35$$

Ikki tarafini -11 ga bo‘ling.

$$x=\frac{-35}{-11}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-35}{-11} kasrini \frac{35}{11} ga soddalashtirish mumkin.

$$x=\frac{35}{11}$$