x+1/2*(x-1/2)=2x-1/4(x+2)+15/4 eching

$$\frac { x + 1 } { 2 } \cdot ( x - \frac { 1 } { 2 } ) = \frac { 2 x - 1 } { 4 } ( x + 2 ) + \frac { 15 } { 4 }$$

x uchun yechish

$$x=-7$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 4 ga, 2,4 ning eng kichik karralisiga ko‘paytiring.

$$2\left(x+1\right)\left(x-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

2 ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(2x+2\right)\left(x-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

2x+2 ifodaning har bir elementini x-\frac{1}{2} ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$2x^{2}+2x\left(-\frac{1}{2}\right)+2x+2\left(-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

2 va 2 ni qisqartiring.

$$2x^{2}-x+2x+2\left(-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

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

$$2x^{2}+x+2\left(-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

2 va 2 ni qisqartiring.

$$2x^{2}+x-1=\left(2x-1\right)\left(x+2\right)+15$$

2x-1 ifodaning har bir elementini x+2 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$2x^{2}+x-1=2x^{2}+4x-x-2+15$$

3x ni olish uchun 4x va -x ni birlashtirish.

$$2x^{2}+x-1=2x^{2}+3x-2+15$$

13 olish uchun -2 va 15'ni qo'shing.

$$2x^{2}+x-1=2x^{2}+3x+13$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$2x^{2}+x-1-2x^{2}=3x+13$$

0 ni olish uchun 2x^{2} va -2x^{2} ni birlashtirish.

$$x-1=3x+13$$

Ikkala tarafdan 3x ni ayirish.

$$x-1-3x=13$$

-2x ni olish uchun x va -3x ni birlashtirish.

$$-2x-1=13$$

1 ni ikki tarafga qo’shing.

$$-2x=13+1$$

14 olish uchun 13 va 1'ni qo'shing.

$$-2x=14$$

Ikki tarafini -2 ga bo‘ling.

$$x=\frac{14}{-2}$$

-7 ni olish uchun 14 ni -2 ga bo‘ling.

$$x=-7$$