12/5(r-2)=2/3[3r-2(2r-1)] eching

$$\frac { 12 } { 5 } ( r - 2 ) = \frac { 2 } { 3 } [ 3 r - 2 ( 2 r - 1 ) ]$$

r uchun yechish

$$r=2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{12}{5} ga r-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{12}{5}r+\frac{12}{5}\left(-2\right)=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

\frac{12}{5}\left(-2\right) ni yagona kasrga aylantiring.

$$\frac{12}{5}r+\frac{12\left(-2\right)}{5}=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

-24 hosil qilish uchun 12 va -2 ni ko'paytirish.

$$\frac{12}{5}r+\frac{-24}{5}=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

\frac{-24}{5} kasri manfiy belgini olib tashlash bilan -\frac{24}{5} sifatida qayta yozilishi mumkin.

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

-2 ga 2r-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(3r-4r+2\right)$$

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

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(-r+2\right)$$

\frac{2}{3} ga -r+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(-1\right)r+\frac{2}{3}\times 2$$

-\frac{2}{3} hosil qilish uchun \frac{2}{3} va -1 ni ko'paytirish.

$$\frac{12}{5}r-\frac{24}{5}=-\frac{2}{3}r+\frac{2}{3}\times 2$$

\frac{2}{3}\times 2 ni yagona kasrga aylantiring.

$$\frac{12}{5}r-\frac{24}{5}=-\frac{2}{3}r+\frac{2\times 2}{3}$$

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

$$\frac{12}{5}r-\frac{24}{5}=-\frac{2}{3}r+\frac{4}{3}$$

\frac{2}{3}r ni ikki tarafga qo’shing.

$$\frac{12}{5}r-\frac{24}{5}+\frac{2}{3}r=\frac{4}{3}$$

\frac{46}{15}r ni olish uchun \frac{12}{5}r va \frac{2}{3}r ni birlashtirish.

$$\frac{46}{15}r-\frac{24}{5}=\frac{4}{3}$$

\frac{24}{5} ni ikki tarafga qo’shing.

$$\frac{46}{15}r=\frac{4}{3}+\frac{24}{5}$$

3 va 5 ning eng kichik umumiy karralisi 15 ga teng. \frac{4}{3} va \frac{24}{5} ni 15 maxraj bilan kasrlarga aylantirib oling.

$$\frac{46}{15}r=\frac{20}{15}+\frac{72}{15}$$

\frac{20}{15} va \frac{72}{15} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{46}{15}r=\frac{20+72}{15}$$

92 olish uchun 20 va 72'ni qo'shing.

$$\frac{46}{15}r=\frac{92}{15}$$

Ikki tarafini \frac{15}{46} va teskari kasri \frac{46}{15} ga ko‘paytiring.

$$r=\frac{92}{15}\times \frac{15}{46}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{92}{15} ni \frac{15}{46} ga ko‘paytiring.

$$r=\frac{92\times 15}{15\times 46}$$

Surat va maxrajdagi ikkala 15 ni qisqartiring.

$$r=\frac{92}{46}$$

2 ni olish uchun 92 ni 46 ga bo‘ling.

$$r=2$$