x/a+1/2a=2x-3/2a+2(1-a) eching

$$\frac { x } { a } + \frac { 1 } { 2 } a = 2 x - \frac { 3 } { 2 } a + 2 ( 1 - a )$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=2a\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&a=\frac{1}{2}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2x+\frac{1}{2}a\times 2a=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

a^{2} hosil qilish uchun a va a ni ko'paytirish.

$$2x+\frac{1}{2}a^{2}\times 2=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

1 hosil qilish uchun \frac{1}{2} va 2 ni ko'paytirish.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

a^{2} hosil qilish uchun a va a ni ko'paytirish.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$2x+a^{2}=4xa-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

-3 hosil qilish uchun -\frac{3}{2} va 2 ni ko'paytirish.

$$2x+a^{2}=4xa-3a^{2}+2\left(1-a\right)\times 2a$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$2x+a^{2}=4xa-3a^{2}+4\left(1-a\right)a$$

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

$$2x+a^{2}=4xa-3a^{2}+\left(4-4a\right)a$$

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

$$2x+a^{2}=4xa-3a^{2}+4a-4a^{2}$$

-7a^{2} ni olish uchun -3a^{2} va -4a^{2} ni birlashtirish.

$$2x+a^{2}=4xa-7a^{2}+4a$$

Ikkala tarafdan 4xa ni ayirish.

$$2x+a^{2}-4xa=-7a^{2}+4a$$

Ikkala tarafdan a^{2} ni ayirish.

$$2x-4xa=-7a^{2}+4a-a^{2}$$

-8a^{2} ni olish uchun -7a^{2} va -a^{2} ni birlashtirish.

$$2x-4xa=-8a^{2}+4a$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2-4a\right)x=-8a^{2}+4a$$

Tenglama standart shaklda.

$$\left(2-4a\right)x=4a-8a^{2}$$

Ikki tarafini 2-4a ga bo‘ling.

$$\frac{\left(2-4a\right)x}{2-4a}=\frac{4a\left(1-2a\right)}{2-4a}$$

2-4a ga bo'lish 2-4a ga ko'paytirishni bekor qiladi.

$$x=\frac{4a\left(1-2a\right)}{2-4a}$$

4a\left(1-2a\right) ni 2-4a ga bo'lish.

$$x=2a$$

x uchun yechish

$$\left\{\begin{matrix}x=2a\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&a=\frac{1}{2}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2x+\frac{1}{2}a\times 2a=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

a^{2} hosil qilish uchun a va a ni ko'paytirish.

$$2x+\frac{1}{2}a^{2}\times 2=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

1 hosil qilish uchun \frac{1}{2} va 2 ni ko'paytirish.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

a^{2} hosil qilish uchun a va a ni ko'paytirish.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$2x+a^{2}=4xa-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

-3 hosil qilish uchun -\frac{3}{2} va 2 ni ko'paytirish.

$$2x+a^{2}=4xa-3a^{2}+2\left(1-a\right)\times 2a$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$2x+a^{2}=4xa-3a^{2}+4\left(1-a\right)a$$

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

$$2x+a^{2}=4xa-3a^{2}+\left(4-4a\right)a$$

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

$$2x+a^{2}=4xa-3a^{2}+4a-4a^{2}$$

-7a^{2} ni olish uchun -3a^{2} va -4a^{2} ni birlashtirish.

$$2x+a^{2}=4xa-7a^{2}+4a$$

Ikkala tarafdan 4xa ni ayirish.

$$2x+a^{2}-4xa=-7a^{2}+4a$$

Ikkala tarafdan a^{2} ni ayirish.

$$2x-4xa=-7a^{2}+4a-a^{2}$$

-8a^{2} ni olish uchun -7a^{2} va -a^{2} ni birlashtirish.

$$2x-4xa=-8a^{2}+4a$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2-4a\right)x=-8a^{2}+4a$$

Tenglama standart shaklda.

$$\left(2-4a\right)x=4a-8a^{2}$$

Ikki tarafini 2-4a ga bo‘ling.

$$\frac{\left(2-4a\right)x}{2-4a}=\frac{4a\left(1-2a\right)}{2-4a}$$

2-4a ga bo'lish 2-4a ga ko'paytirishni bekor qiladi.

$$x=\frac{4a\left(1-2a\right)}{2-4a}$$

4a\left(1-2a\right) ni 2-4a ga bo'lish.

$$x=2a$$

a uchun yechish

$$\left\{\begin{matrix}\\a=\frac{1}{2}=0,5\text{, }&\text{unconditionally}\\a=\frac{x}{2}\text{, }&x\neq 0\end{matrix}\right,$$