3/2(x+5)-1/3(x+2)=9/2 eching

$$\frac{ 3 }{ 2 } (x+5)- \frac{ 1 }{ 3 } (x+2)= \frac{ 9 }{ 2 }$$

x uchun yechish

$$x=-2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{3}{2} ga x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{2}x+\frac{3}{2}\times 5-\frac{1}{3}\left(x+2\right)=\frac{9}{2}$$

\frac{3}{2}\times 5 ni yagona kasrga aylantiring.

$$\frac{3}{2}x+\frac{3\times 5}{2}-\frac{1}{3}\left(x+2\right)=\frac{9}{2}$$

15 hosil qilish uchun 3 va 5 ni ko'paytirish.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}\left(x+2\right)=\frac{9}{2}$$

-\frac{1}{3} ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}x-\frac{1}{3}\times 2=\frac{9}{2}$$

-\frac{1}{3}\times 2 ni yagona kasrga aylantiring.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}x+\frac{-2}{3}=\frac{9}{2}$$

\frac{-2}{3} kasri manfiy belgini olib tashlash bilan -\frac{2}{3} sifatida qayta yozilishi mumkin.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{3}x-\frac{2}{3}=\frac{9}{2}$$

\frac{7}{6}x ni olish uchun \frac{3}{2}x va -\frac{1}{3}x ni birlashtirish.

$$\frac{7}{6}x+\frac{15}{2}-\frac{2}{3}=\frac{9}{2}$$

2 va 3 ning eng kichik umumiy karralisi 6 ga teng. \frac{15}{2} va \frac{2}{3} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\frac{7}{6}x+\frac{45}{6}-\frac{4}{6}=\frac{9}{2}$$

\frac{45}{6} va \frac{4}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{7}{6}x+\frac{45-4}{6}=\frac{9}{2}$$

41 olish uchun 45 dan 4 ni ayirish.

$$\frac{7}{6}x+\frac{41}{6}=\frac{9}{2}$$

Ikkala tarafdan \frac{41}{6} ni ayirish.

$$\frac{7}{6}x=\frac{9}{2}-\frac{41}{6}$$

2 va 6 ning eng kichik umumiy karralisi 6 ga teng. \frac{9}{2} va \frac{41}{6} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\frac{7}{6}x=\frac{27}{6}-\frac{41}{6}$$

\frac{27}{6} va \frac{41}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{7}{6}x=\frac{27-41}{6}$$

-14 olish uchun 27 dan 41 ni ayirish.

$$\frac{7}{6}x=\frac{-14}{6}$$

\frac{-14}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{7}{6}x=-\frac{7}{3}$$

Ikki tarafini \frac{6}{7} va teskari kasri \frac{7}{6} ga ko‘paytiring.

$$x=-\frac{7}{3}\times \frac{6}{7}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{7}{3} ni \frac{6}{7} ga ko‘paytiring.

$$x=\frac{-7\times 6}{3\times 7}$$

\frac{-7\times 6}{3\times 7} kasridagi ko‘paytirishlarni bajaring.

$$x=\frac{-42}{21}$$

-2 ni olish uchun -42 ni 21 ga bo‘ling.

$$x=-2$$