(x-2)-1/2(x+1)=5/6(x+2) eching

$$( x - 2 ) - \frac { 1 } { 2 } ( x + 1 ) = \frac { 5 } { 6 } ( x + 2 )$$

x uchun yechish

$$x = -\frac{25}{2} = -12\frac{1}{2} = -12,5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x-2-\frac{1}{2}x-\frac{1}{2}=\frac{5}{6}\left(x+2\right)$$

\frac{1}{2}x ni olish uchun x va -\frac{1}{2}x ni birlashtirish.

$$\frac{1}{2}x-2-\frac{1}{2}=\frac{5}{6}\left(x+2\right)$$

-2 ni -\frac{4}{2} kasrga o‘giring.

$$\frac{1}{2}x-\frac{4}{2}-\frac{1}{2}=\frac{5}{6}\left(x+2\right)$$

-\frac{4}{2} va \frac{1}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{1}{2}x+\frac{-4-1}{2}=\frac{5}{6}\left(x+2\right)$$

-5 olish uchun -4 dan 1 ni ayirish.

$$\frac{1}{2}x-\frac{5}{2}=\frac{5}{6}\left(x+2\right)$$

\frac{5}{6} ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{2}x-\frac{5}{2}=\frac{5}{6}x+\frac{5}{6}\times 2$$

\frac{5}{6}\times 2 ni yagona kasrga aylantiring.

$$\frac{1}{2}x-\frac{5}{2}=\frac{5}{6}x+\frac{5\times 2}{6}$$

10 hosil qilish uchun 5 va 2 ni ko'paytirish.

$$\frac{1}{2}x-\frac{5}{2}=\frac{5}{6}x+\frac{10}{6}$$

\frac{10}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}x-\frac{5}{2}=\frac{5}{6}x+\frac{5}{3}$$

Ikkala tarafdan \frac{5}{6}x ni ayirish.

$$\frac{1}{2}x-\frac{5}{2}-\frac{5}{6}x=\frac{5}{3}$$

-\frac{1}{3}x ni olish uchun \frac{1}{2}x va -\frac{5}{6}x ni birlashtirish.

$$-\frac{1}{3}x-\frac{5}{2}=\frac{5}{3}$$

\frac{5}{2} ni ikki tarafga qo’shing.

$$-\frac{1}{3}x=\frac{5}{3}+\frac{5}{2}$$

3 va 2 ning eng kichik umumiy karralisi 6 ga teng. \frac{5}{3} va \frac{5}{2} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$-\frac{1}{3}x=\frac{10}{6}+\frac{15}{6}$$

\frac{10}{6} va \frac{15}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$-\frac{1}{3}x=\frac{10+15}{6}$$

25 olish uchun 10 va 15'ni qo'shing.

$$-\frac{1}{3}x=\frac{25}{6}$$

Ikki tarafini -3 va teskari kasri -\frac{1}{3} ga ko‘paytiring.

$$x=\frac{25}{6}\left(-3\right)$$

\frac{25}{6}\left(-3\right) ni yagona kasrga aylantiring.

$$x=\frac{25\left(-3\right)}{6}$$

-75 hosil qilish uchun 25 va -3 ni ko'paytirish.

$$x=\frac{-75}{6}$$

\frac{-75}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{25}{2}$$