2/3left(left(2x-1right)left(x-4right)+3left(x-1/3right)left(1/3+xright)right)=2/3left(5x^2-xright)+frac{14}{9} eching

$$\frac{ 2 }{ 3 } \left( \left( 2x-1 \right) \left( x-4 \right) +3 \left( x- \frac{ 1 }{ 3 } \right) \left( \frac{ 1 }{ 3 } +x \right) \right) = \frac{ 2 }{ 3 } \left( 5 { x }^{ 2 } -x \right) + \frac{ 14 }{ 9 }$$

x uchun yechish

$$x=\frac{1}{6}\approx 0,166666667$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2x-1 ga x-4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{2}{3}\left(2x^{2}-9x+4+3\left(x-\frac{1}{3}\right)\left(\frac{1}{3}+x\right)\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

3 ga x-\frac{1}{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{2}{3}\left(2x^{2}-9x+4+\left(3x-1\right)\left(\frac{1}{3}+x\right)\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

3x-1 ga \frac{1}{3}+x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{2}{3}\left(2x^{2}-9x+4+3x^{2}-\frac{1}{3}\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

5x^{2} ni olish uchun 2x^{2} va 3x^{2} ni birlashtirish.

$$\frac{2}{3}\left(5x^{2}-9x+4-\frac{1}{3}\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

\frac{11}{3} olish uchun 4 dan \frac{1}{3} ni ayirish.

$$\frac{2}{3}\left(5x^{2}-9x+\frac{11}{3}\right)=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

\frac{2}{3} ga 5x^{2}-9x+\frac{11}{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{10}{3}x^{2}-6x+\frac{22}{9}=\frac{2}{3}\left(5x^{2}-x\right)+\frac{14}{9}$$

\frac{2}{3} ga 5x^{2}-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{10}{3}x^{2}-6x+\frac{22}{9}=\frac{10}{3}x^{2}-\frac{2}{3}x+\frac{14}{9}$$

Ikkala tarafdan \frac{10}{3}x^{2} ni ayirish.

$$\frac{10}{3}x^{2}-6x+\frac{22}{9}-\frac{10}{3}x^{2}=-\frac{2}{3}x+\frac{14}{9}$$

0 ni olish uchun \frac{10}{3}x^{2} va -\frac{10}{3}x^{2} ni birlashtirish.

$$-6x+\frac{22}{9}=-\frac{2}{3}x+\frac{14}{9}$$

\frac{2}{3}x ni ikki tarafga qo’shing.

$$-6x+\frac{22}{9}+\frac{2}{3}x=\frac{14}{9}$$

-\frac{16}{3}x ni olish uchun -6x va \frac{2}{3}x ni birlashtirish.

$$-\frac{16}{3}x+\frac{22}{9}=\frac{14}{9}$$

Ikkala tarafdan \frac{22}{9} ni ayirish.

$$-\frac{16}{3}x=\frac{14}{9}-\frac{22}{9}$$

-\frac{8}{9} olish uchun \frac{14}{9} dan \frac{22}{9} ni ayirish.

$$-\frac{16}{3}x=-\frac{8}{9}$$

Ikki tarafini -\frac{3}{16} va teskari kasri -\frac{16}{3} ga ko‘paytiring.

$$x=-\frac{8}{9}\left(-\frac{3}{16}\right)$$

\frac{1}{6} hosil qilish uchun -\frac{8}{9} va -\frac{3}{16} ni ko'paytirish.

$$x=\frac{1}{6}$$