x-1/3-5x+2/8=2x-3/6+x-3/4 eching

$$\frac { x - 1 } { 3 } - \frac { 5 x + 2 } { 8 } = \frac { 2 x - 3 } { 6 } + \frac { x - 3 } { 4 }$$

x uchun yechish

$$x=\frac{16}{21}\approx 0,761904762$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 24 ga, 3,8,6,4 ning eng kichik karralisiga ko‘paytiring.

$$8\left(x-1\right)-3\left(5x+2\right)=4\left(2x-3\right)+6\left(x-3\right)$$

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

$$8x-8-3\left(5x+2\right)=4\left(2x-3\right)+6\left(x-3\right)$$

-3 ga 5x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8x-8-15x-6=4\left(2x-3\right)+6\left(x-3\right)$$

-7x ni olish uchun 8x va -15x ni birlashtirish.

$$-7x-8-6=4\left(2x-3\right)+6\left(x-3\right)$$

-14 olish uchun -8 dan 6 ni ayirish.

$$-7x-14=4\left(2x-3\right)+6\left(x-3\right)$$

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

$$-7x-14=8x-12+6\left(x-3\right)$$

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

$$-7x-14=8x-12+6x-18$$

14x ni olish uchun 8x va 6x ni birlashtirish.

$$-7x-14=14x-12-18$$

-30 olish uchun -12 dan 18 ni ayirish.

$$-7x-14=14x-30$$

Ikkala tarafdan 14x ni ayirish.

$$-7x-14-14x=-30$$

-21x ni olish uchun -7x va -14x ni birlashtirish.

$$-21x-14=-30$$

14 ni ikki tarafga qo’shing.

$$-21x=-30+14$$

-16 olish uchun -30 va 14'ni qo'shing.

$$-21x=-16$$

Ikki tarafini -21 ga bo‘ling.

$$x=\frac{-16}{-21}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-16}{-21} kasrini \frac{16}{21} ga soddalashtirish mumkin.

$$x=\frac{16}{21}$$