1/3(x-6)<x+8 eching

$$\frac { 1 } { 3 } ( x - 6 ) < x + 8$$

x uchun yechish

$$x>-15$$

Yechim qadamlari

\frac{1}{3} ga x-6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{3}x+\frac{1}{3}\left(-6\right)<x+8$$

\frac{-6}{3} hosil qilish uchun \frac{1}{3} va -6 ni ko'paytirish.

$$\frac{1}{3}x+\frac{-6}{3}<x+8$$

-2 ni olish uchun -6 ni 3 ga bo‘ling.

$$\frac{1}{3}x-2<x+8$$

Ikkala tarafdan x ni ayirish.

$$\frac{1}{3}x-2-x<8$$

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

$$-\frac{2}{3}x-2<8$$

2 ni ikki tarafga qo’shing.

$$-\frac{2}{3}x<8+2$$

10 olish uchun 8 va 2'ni qo'shing.

$$-\frac{2}{3}x<10$$

Ikki tarafini -\frac{3}{2} va teskari kasri -\frac{2}{3} ga ko‘paytiring. -\frac{2}{3} <0 bo‘lganda, tengsizlikning yo‘nalishi o‘zgargan bo‘ladi.

$$x>10\left(-\frac{3}{2}\right)$$

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

$$x>\frac{10\left(-3\right)}{2}$$

-30 hosil qilish uchun 10 va -3 ni ko'paytirish.

$$x>\frac{-30}{2}$$

-15 ni olish uchun -30 ni 2 ga bo‘ling.

$$x>-15$$