(m)x-4/8+x+1/2=x+7/2-x-5/8-frac{x+6}{4} eching

$$( m ) \frac { x - 4 } { 8 } + \frac { x + 1 } { 2 } = \frac { x + 7 } { 2 } - \frac { x - 5 } { 8 } - \frac { x + 6 } { 4 }$$

m uchun yechish

$$m=-\frac{3x-17}{x-4}$$

$$x\neq 4$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 8 ga, 8,2,4 ning eng kichik karralisiga ko‘paytiring.

$$m\left(x-4\right)+4\left(x+1\right)=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

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

$$mx-4m+4\left(x+1\right)=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

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

$$mx-4m+4x+4=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

4 ga x+7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mx-4m+4x+4=4x+28-\left(x-5\right)-2\left(x+6\right)$$

x-5 teskarisini topish uchun har birining teskarisini toping.

$$mx-4m+4x+4=4x+28-x+5-2\left(x+6\right)$$

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

$$mx-4m+4x+4=3x+28+5-2\left(x+6\right)$$

33 olish uchun 28 va 5'ni qo'shing.

$$mx-4m+4x+4=3x+33-2\left(x+6\right)$$

-2 ga x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mx-4m+4x+4=3x+33-2x-12$$

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

$$mx-4m+4x+4=x+33-12$$

21 olish uchun 33 dan 12 ni ayirish.

$$mx-4m+4x+4=x+21$$

Ikkala tarafdan 4x ni ayirish.

$$mx-4m+4=x+21-4x$$

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

$$mx-4m+4=-3x+21$$

Ikkala tarafdan 4 ni ayirish.

$$mx-4m=-3x+21-4$$

17 olish uchun 21 dan 4 ni ayirish.

$$mx-4m=-3x+17$$

m'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x-4\right)m=-3x+17$$

Tenglama standart shaklda.

$$\left(x-4\right)m=17-3x$$

Ikki tarafini x-4 ga bo‘ling.

$$\frac{\left(x-4\right)m}{x-4}=\frac{17-3x}{x-4}$$

x-4 ga bo'lish x-4 ga ko'paytirishni bekor qiladi.

$$m=\frac{17-3x}{x-4}$$

x uchun yechish

$$x=\frac{4m+17}{m+3}$$

$$m\neq -3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 8 ga, 8,2,4 ning eng kichik karralisiga ko‘paytiring.

$$m\left(x-4\right)+4\left(x+1\right)=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

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

$$mx-4m+4\left(x+1\right)=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

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

$$mx-4m+4x+4=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

4 ga x+7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mx-4m+4x+4=4x+28-\left(x-5\right)-2\left(x+6\right)$$

x-5 teskarisini topish uchun har birining teskarisini toping.

$$mx-4m+4x+4=4x+28-x+5-2\left(x+6\right)$$

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

$$mx-4m+4x+4=3x+28+5-2\left(x+6\right)$$

33 olish uchun 28 va 5'ni qo'shing.

$$mx-4m+4x+4=3x+33-2\left(x+6\right)$$

-2 ga x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mx-4m+4x+4=3x+33-2x-12$$

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

$$mx-4m+4x+4=x+33-12$$

21 olish uchun 33 dan 12 ni ayirish.

$$mx-4m+4x+4=x+21$$

Ikkala tarafdan x ni ayirish.

$$mx-4m+4x+4-x=21$$

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

$$mx-4m+3x+4=21$$

4m ni ikki tarafga qo’shing.

$$mx+3x+4=21+4m$$

Ikkala tarafdan 4 ni ayirish.

$$mx+3x=21+4m-4$$

17 olish uchun 21 dan 4 ni ayirish.

$$mx+3x=17+4m$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(m+3\right)x=17+4m$$

Tenglama standart shaklda.

$$\left(m+3\right)x=4m+17$$

Ikki tarafini m+3 ga bo‘ling.

$$\frac{\left(m+3\right)x}{m+3}=\frac{4m+17}{m+3}$$

m+3 ga bo'lish m+3 ga ko'paytirishni bekor qiladi.

$$x=\frac{4m+17}{m+3}$$