2g(x-2)=3f(x-2) eching

$$2 g ( x - 2 ) = 3 f ( x - 2 )$$

f uchun yechish (complex solution)

$$\left\{\begin{matrix}\\f=\frac{2g}{3}\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=2\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2gx-4g=3f\left(x-2\right)$$

3f ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2gx-4g=3fx-6f$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$3fx-6f=2gx-4g$$

f'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3x-6\right)f=2gx-4g$$

Ikki tarafini 3x-6 ga bo‘ling.

$$\frac{\left(3x-6\right)f}{3x-6}=\frac{2g\left(x-2\right)}{3x-6}$$

3x-6 ga bo'lish 3x-6 ga ko'paytirishni bekor qiladi.

$$f=\frac{2g\left(x-2\right)}{3x-6}$$

2g\left(-2+x\right) ni 3x-6 ga bo'lish.

$$f=\frac{2g}{3}$$

g uchun yechish (complex solution)

$$\left\{\begin{matrix}\\g=\frac{3f}{2}\text{, }&\text{unconditionally}\\g\in \mathrm{C}\text{, }&x=2\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2gx-4g=3f\left(x-2\right)$$

3f ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2gx-4g=3fx-6f$$

g'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2x-4\right)g=3fx-6f$$

Ikki tarafini 2x-4 ga bo‘ling.

$$\frac{\left(2x-4\right)g}{2x-4}=\frac{3f\left(x-2\right)}{2x-4}$$

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

$$g=\frac{3f\left(x-2\right)}{2x-4}$$

3f\left(-2+x\right) ni 2x-4 ga bo'lish.

$$g=\frac{3f}{2}$$

f uchun yechish

$$\left\{\begin{matrix}\\f=\frac{2g}{3}\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=2\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2gx-4g=3f\left(x-2\right)$$

3f ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2gx-4g=3fx-6f$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$3fx-6f=2gx-4g$$

f'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3x-6\right)f=2gx-4g$$

Ikki tarafini 3x-6 ga bo‘ling.

$$\frac{\left(3x-6\right)f}{3x-6}=\frac{2g\left(x-2\right)}{3x-6}$$

3x-6 ga bo'lish 3x-6 ga ko'paytirishni bekor qiladi.

$$f=\frac{2g\left(x-2\right)}{3x-6}$$

2g\left(-2+x\right) ni 3x-6 ga bo'lish.

$$f=\frac{2g}{3}$$

g uchun yechish

$$\left\{\begin{matrix}\\g=\frac{3f}{2}\text{, }&\text{unconditionally}\\g\in \mathrm{R}\text{, }&x=2\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2gx-4g=3f\left(x-2\right)$$

3f ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2gx-4g=3fx-6f$$

g'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2x-4\right)g=3fx-6f$$

Ikki tarafini 2x-4 ga bo‘ling.

$$\frac{\left(2x-4\right)g}{2x-4}=\frac{3f\left(x-2\right)}{2x-4}$$

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

$$g=\frac{3f\left(x-2\right)}{2x-4}$$

3f\left(-2+x\right) ni 2x-4 ga bo'lish.

$$g=\frac{3f}{2}$$