1/4(3-2x)-2>1/3x eching

$$\frac { 1 } { 4 } ( 3 - 2 x ) - 2 > \frac { 1 } { 3 } x$$

x uchun yechish

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

Yechim qadamlari

\frac{1}{4} ga 3-2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

\frac{3}{4} hosil qilish uchun \frac{1}{4} va 3 ni ko'paytirish.

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

\frac{-2}{4} hosil qilish uchun \frac{1}{4} va -2 ni ko'paytirish.

$$\frac{3}{4}+\frac{-2}{4}x-2>\frac{1}{3}x$$

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

$$\frac{3}{4}-\frac{1}{2}x-2>\frac{1}{3}x$$

2 ni \frac{8}{4} kasrga o‘giring.

$$\frac{3}{4}-\frac{1}{2}x-\frac{8}{4}>\frac{1}{3}x$$

\frac{3}{4} va \frac{8}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{3-8}{4}-\frac{1}{2}x>\frac{1}{3}x$$

-5 olish uchun 3 dan 8 ni ayirish.

$$-\frac{5}{4}-\frac{1}{2}x>\frac{1}{3}x$$

Ikkala tarafdan \frac{1}{3}x ni ayirish.

$$-\frac{5}{4}-\frac{1}{2}x-\frac{1}{3}x>0$$

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

$$-\frac{5}{4}-\frac{5}{6}x>0$$

\frac{5}{4} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$-\frac{5}{6}x>\frac{5}{4}$$

Ikki tarafini -\frac{6}{5} va teskari kasri -\frac{5}{6} ga ko‘paytiring. -\frac{5}{6} manfiy boʻlgani uchun tengsizlikning yo‘nalishi o‘zgaradi.

$$x<\frac{5}{4}\left(-\frac{6}{5}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{4} ni -\frac{6}{5} ga ko‘paytiring.

$$x<\frac{5\left(-6\right)}{4\times 5}$$

Surat va maxrajdagi ikkala 5 ni qisqartiring.

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

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

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