4x-1/3-9x-4/7-x/2+10/7=frac{x-5}{6}+frac{2x+3}{14} eching

$$\frac { 4 x - 1 } { 3 } - \frac { 9 x - 4 } { 7 } - \frac { x } { 2 } + \frac { 10 } { 7 } = \frac { x - 5 } { 6 } + \frac { 2 x + 3 } { 14 }$$

x uchun yechish

$$x=3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 42 ga, 3,7,2,6,14 ning eng kichik karralisiga ko‘paytiring.

$$14\left(4x-1\right)-6\left(9x-4\right)-21x+60=7\left(x-5\right)+3\left(2x+3\right)$$

14 ga 4x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$56x-14-6\left(9x-4\right)-21x+60=7\left(x-5\right)+3\left(2x+3\right)$$

-6 ga 9x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$56x-14-54x+24-21x+60=7\left(x-5\right)+3\left(2x+3\right)$$

2x ni olish uchun 56x va -54x ni birlashtirish.

$$2x-14+24-21x+60=7\left(x-5\right)+3\left(2x+3\right)$$

10 olish uchun -14 va 24'ni qo'shing.

$$2x+10-21x+60=7\left(x-5\right)+3\left(2x+3\right)$$

-19x ni olish uchun 2x va -21x ni birlashtirish.

$$-19x+10+60=7\left(x-5\right)+3\left(2x+3\right)$$

70 olish uchun 10 va 60'ni qo'shing.

$$-19x+70=7\left(x-5\right)+3\left(2x+3\right)$$

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

$$-19x+70=7x-35+3\left(2x+3\right)$$

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

$$-19x+70=7x-35+6x+9$$

13x ni olish uchun 7x va 6x ni birlashtirish.

$$-19x+70=13x-35+9$$

-26 olish uchun -35 va 9'ni qo'shing.

$$-19x+70=13x-26$$

Ikkala tarafdan 13x ni ayirish.

$$-19x+70-13x=-26$$

-32x ni olish uchun -19x va -13x ni birlashtirish.

$$-32x+70=-26$$

Ikkala tarafdan 70 ni ayirish.

$$-32x=-26-70$$

-96 olish uchun -26 dan 70 ni ayirish.

$$-32x=-96$$

Ikki tarafini -32 ga bo‘ling.

$$x=\frac{-96}{-32}$$

3 ni olish uchun -96 ni -32 ga bo‘ling.

$$x=3$$