3/2(x-2)<3/4(x-8) eching

$$\frac{ 3 }{ 2 } (x-2) < \frac{ 3 }{ 4 } (x-8)$$

x uchun yechish

$$x<-4$$

Yechim qadamlari

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

$$\frac{3}{2}x+\frac{3}{2}\left(-2\right)<\frac{3}{4}\left(x-8\right)$$

\frac{3}{2}\left(-2\right) ni yagona kasrga aylantiring.

$$\frac{3}{2}x+\frac{3\left(-2\right)}{2}<\frac{3}{4}\left(x-8\right)$$

-6 hosil qilish uchun 3 va -2 ni ko'paytirish.

$$\frac{3}{2}x+\frac{-6}{2}<\frac{3}{4}\left(x-8\right)$$

-3 ni olish uchun -6 ni 2 ga bo‘ling.

$$\frac{3}{2}x-3<\frac{3}{4}\left(x-8\right)$$

\frac{3}{4} ga x-8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{2}x-3<\frac{3}{4}x+\frac{3}{4}\left(-8\right)$$

\frac{3}{4}\left(-8\right) ni yagona kasrga aylantiring.

$$\frac{3}{2}x-3<\frac{3}{4}x+\frac{3\left(-8\right)}{4}$$

-24 hosil qilish uchun 3 va -8 ni ko'paytirish.

$$\frac{3}{2}x-3<\frac{3}{4}x+\frac{-24}{4}$$

-6 ni olish uchun -24 ni 4 ga bo‘ling.

$$\frac{3}{2}x-3<\frac{3}{4}x-6$$

Ikkala tarafdan \frac{3}{4}x ni ayirish.

$$\frac{3}{2}x-3-\frac{3}{4}x<-6$$

\frac{3}{4}x ni olish uchun \frac{3}{2}x va -\frac{3}{4}x ni birlashtirish.

$$\frac{3}{4}x-3<-6$$

3 ni ikki tarafga qo’shing.

$$\frac{3}{4}x<-6+3$$

-3 olish uchun -6 va 3'ni qo'shing.

$$\frac{3}{4}x<-3$$

Ikki tarafini \frac{4}{3} va teskari kasri \frac{3}{4} ga ko‘paytiring. \frac{3}{4} musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$x<-3\times \frac{4}{3}$$

-3 ni \frac{4}{3} marotabaga ko'paytirish.

$$x<-4$$