2/5[x-5/3(x+4)]=x-3/3-2/3(x+2) eching

$$\frac { 2 } { 5 } [ x - \frac { 5 } { 3 } ( x + 4 ) ] = \frac { x - 3 } { 3 } - \frac { 2 } { 3 } ( x + 2 )$$

x uchun yechish

$$x=5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 15 ga, 5,3 ning eng kichik karralisiga ko‘paytiring.

$$6\left(x-\frac{5}{3}\left(x+4\right)\right)=5\left(x-3\right)-10\left(x+2\right)$$

-\frac{5}{3} ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6\left(x-\frac{5}{3}x-\frac{5}{3}\times 4\right)=5\left(x-3\right)-10\left(x+2\right)$$

-\frac{5}{3}\times 4 ni yagona kasrga aylantiring.

$$6\left(x-\frac{5}{3}x+\frac{-5\times 4}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

-20 hosil qilish uchun -5 va 4 ni ko'paytirish.

$$6\left(x-\frac{5}{3}x+\frac{-20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

\frac{-20}{3} kasri manfiy belgini olib tashlash bilan -\frac{20}{3} sifatida qayta yozilishi mumkin.

$$6\left(x-\frac{5}{3}x-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

-\frac{2}{3}x ni olish uchun x va -\frac{5}{3}x ni birlashtirish.

$$6\left(-\frac{2}{3}x-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

6 ga -\frac{2}{3}x-\frac{20}{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6\left(-\frac{2}{3}\right)x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

6\left(-\frac{2}{3}\right) ni yagona kasrga aylantiring.

$$\frac{6\left(-2\right)}{3}x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

-12 hosil qilish uchun 6 va -2 ni ko'paytirish.

$$\frac{-12}{3}x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

-4 ni olish uchun -12 ni 3 ga bo‘ling.

$$-4x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

6\left(-\frac{20}{3}\right) ni yagona kasrga aylantiring.

$$-4x+\frac{6\left(-20\right)}{3}=5\left(x-3\right)-10\left(x+2\right)$$

-120 hosil qilish uchun 6 va -20 ni ko'paytirish.

$$-4x+\frac{-120}{3}=5\left(x-3\right)-10\left(x+2\right)$$

-40 ni olish uchun -120 ni 3 ga bo‘ling.

$$-4x-40=5\left(x-3\right)-10\left(x+2\right)$$

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

$$-4x-40=5x-15-10\left(x+2\right)$$

-10 ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-4x-40=5x-15-10x-20$$

-5x ni olish uchun 5x va -10x ni birlashtirish.

$$-4x-40=-5x-15-20$$

-35 olish uchun -15 dan 20 ni ayirish.

$$-4x-40=-5x-35$$

5x ni ikki tarafga qo’shing.

$$-4x-40+5x=-35$$

x ni olish uchun -4x va 5x ni birlashtirish.

$$x-40=-35$$

40 ni ikki tarafga qo’shing.

$$x=-35+40$$

5 olish uchun -35 va 40'ni qo'shing.

$$x=5$$