2/3(4x-1)-[4x-1-3x/2]=x-7/2 eching

$$\frac { 2 } { 3 } ( 4 x - 1 ) - [ 4 x - \frac { 1 - 3 x } { 2 } ] = \frac { x - 7 } { 2 }$$

x uchun yechish

$$x=1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$4\left(4x-1\right)-6\left(4x-\frac{1-3x}{2}\right)=3\left(x-7\right)$$

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

$$16x-4-6\left(4x-\frac{1-3x}{2}\right)=3\left(x-7\right)$$

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

$$16x-4-6\left(4x-\frac{1-3x}{2}\right)=3x-21$$

\frac{1}{2}-\frac{3}{2}x natijani olish uchun 1-3x ning har bir ifodasini 2 ga bo‘ling.

$$16x-4-6\left(4x-\left(\frac{1}{2}-\frac{3}{2}x\right)\right)=3x-21$$

\frac{1}{2}-\frac{3}{2}x teskarisini topish uchun har birining teskarisini toping.

$$16x-4-6\left(4x-\frac{1}{2}-\left(-\frac{3}{2}x\right)\right)=3x-21$$

-\frac{3}{2}x ning teskarisi \frac{3}{2}x ga teng.

$$16x-4-6\left(4x-\frac{1}{2}+\frac{3}{2}x\right)=3x-21$$

\frac{11}{2}x ni olish uchun 4x va \frac{3}{2}x ni birlashtirish.

$$16x-4-6\left(\frac{11}{2}x-\frac{1}{2}\right)=3x-21$$

-6 ga \frac{11}{2}x-\frac{1}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16x-4-6\times \frac{11}{2}x-6\left(-\frac{1}{2}\right)=3x-21$$

-6\times \frac{11}{2} ni yagona kasrga aylantiring.

$$16x-4+\frac{-6\times 11}{2}x-6\left(-\frac{1}{2}\right)=3x-21$$

-66 hosil qilish uchun -6 va 11 ni ko'paytirish.

$$16x-4+\frac{-66}{2}x-6\left(-\frac{1}{2}\right)=3x-21$$

-33 ni olish uchun -66 ni 2 ga bo‘ling.

$$16x-4-33x-6\left(-\frac{1}{2}\right)=3x-21$$

-6\left(-\frac{1}{2}\right) ni yagona kasrga aylantiring.

$$16x-4-33x+\frac{-6\left(-1\right)}{2}=3x-21$$

6 hosil qilish uchun -6 va -1 ni ko'paytirish.

$$16x-4-33x+\frac{6}{2}=3x-21$$

3 ni olish uchun 6 ni 2 ga bo‘ling.

$$16x-4-33x+3=3x-21$$

-17x ni olish uchun 16x va -33x ni birlashtirish.

$$-17x-4+3=3x-21$$

-1 olish uchun -4 va 3'ni qo'shing.

$$-17x-1=3x-21$$

Ikkala tarafdan 3x ni ayirish.

$$-17x-1-3x=-21$$

-20x ni olish uchun -17x va -3x ni birlashtirish.

$$-20x-1=-21$$

1 ni ikki tarafga qo’shing.

$$-20x=-21+1$$

-20 olish uchun -21 va 1'ni qo'shing.

$$-20x=-20$$

Ikki tarafini -20 ga bo‘ling.

$$x=\frac{-20}{-20}$$

1 ni olish uchun -20 ni -20 ga bo‘ling.

$$x=1$$