1/2(x-1)=2-1/5(x+2) eching

$$\frac { 1 } { 2 } ( x - 1 ) = 2 - \frac { 1 } { 5 } ( x + 2 )$$

x uchun yechish

$$x=3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{1}{2} ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{2}x+\frac{1}{2}\left(-1\right)=2-\frac{1}{5}\left(x+2\right)$$

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

$$\frac{1}{2}x-\frac{1}{2}=2-\frac{1}{5}\left(x+2\right)$$

-\frac{1}{5} ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{2}x-\frac{1}{2}=2-\frac{1}{5}x-\frac{1}{5}\times 2$$

-\frac{1}{5}\times 2 ni yagona kasrga aylantiring.

$$\frac{1}{2}x-\frac{1}{2}=2-\frac{1}{5}x+\frac{-2}{5}$$

\frac{-2}{5} kasri manfiy belgini olib tashlash bilan -\frac{2}{5} sifatida qayta yozilishi mumkin.

$$\frac{1}{2}x-\frac{1}{2}=2-\frac{1}{5}x-\frac{2}{5}$$

2 ni \frac{10}{5} kasrga o‘giring.

$$\frac{1}{2}x-\frac{1}{2}=\frac{10}{5}-\frac{1}{5}x-\frac{2}{5}$$

\frac{10}{5} va \frac{2}{5} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{1}{2}x-\frac{1}{2}=\frac{10-2}{5}-\frac{1}{5}x$$

8 olish uchun 10 dan 2 ni ayirish.

$$\frac{1}{2}x-\frac{1}{2}=\frac{8}{5}-\frac{1}{5}x$$

\frac{1}{5}x ni ikki tarafga qo’shing.

$$\frac{1}{2}x-\frac{1}{2}+\frac{1}{5}x=\frac{8}{5}$$

\frac{7}{10}x ni olish uchun \frac{1}{2}x va \frac{1}{5}x ni birlashtirish.

$$\frac{7}{10}x-\frac{1}{2}=\frac{8}{5}$$

\frac{1}{2} ni ikki tarafga qo’shing.

$$\frac{7}{10}x=\frac{8}{5}+\frac{1}{2}$$

5 va 2 ning eng kichik umumiy karralisi 10 ga teng. \frac{8}{5} va \frac{1}{2} ni 10 maxraj bilan kasrlarga aylantirib oling.

$$\frac{7}{10}x=\frac{16}{10}+\frac{5}{10}$$

\frac{16}{10} va \frac{5}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{7}{10}x=\frac{16+5}{10}$$

21 olish uchun 16 va 5'ni qo'shing.

$$\frac{7}{10}x=\frac{21}{10}$$

Ikki tarafini \frac{10}{7} va teskari kasri \frac{7}{10} ga ko‘paytiring.

$$x=\frac{21}{10}\times \frac{10}{7}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{21}{10} ni \frac{10}{7} ga ko‘paytiring.

$$x=\frac{21\times 10}{10\times 7}$$

Surat va maxrajdagi ikkala 10 ni qisqartiring.

$$x=\frac{21}{7}$$

3 ni olish uchun 21 ni 7 ga bo‘ling.

$$x=3$$