9x-1<3/4(16x-2) eching

$$9 x - 1 < \frac { 3 } { 4 } ( 16 x - 2 )$$

x uchun yechish

$$x>\frac{1}{6}$$

Yechim qadamlari

\frac{3}{4} ga 16x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9x-1<\frac{3}{4}\times 16x+\frac{3}{4}\left(-2\right)$$

\frac{3}{4}\times 16 ni yagona kasrga aylantiring.

$$9x-1<\frac{3\times 16}{4}x+\frac{3}{4}\left(-2\right)$$

48 hosil qilish uchun 3 va 16 ni ko'paytirish.

$$9x-1<\frac{48}{4}x+\frac{3}{4}\left(-2\right)$$

12 ni olish uchun 48 ni 4 ga bo‘ling.

$$9x-1<12x+\frac{3}{4}\left(-2\right)$$

\frac{3}{4}\left(-2\right) ni yagona kasrga aylantiring.

$$9x-1<12x+\frac{3\left(-2\right)}{4}$$

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

$$9x-1<12x+\frac{-6}{4}$$

\frac{-6}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$9x-1<12x-\frac{3}{2}$$

Ikkala tarafdan 12x ni ayirish.

$$9x-1-12x<-\frac{3}{2}$$

-3x ni olish uchun 9x va -12x ni birlashtirish.

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

1 ni ikki tarafga qo’shing.

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

1 ni \frac{2}{2} kasrga o‘giring.

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

-\frac{3}{2} va \frac{2}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

-1 olish uchun -3 va 2'ni qo'shing.

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

Ikki tarafini -3 ga bo‘ling. -3 manfiy boʻlgani uchun tengsizlikning yo‘nalishi o‘zgaradi.

$$x>\frac{-\frac{1}{2}}{-3}$$

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

$$x>\frac{-1}{2\left(-3\right)}$$

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

$$x>\frac{-1}{-6}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-1}{-6} kasrini \frac{1}{6} ga soddalashtirish mumkin.

$$x>\frac{1}{6}$$