1-x+3/2>x-2/3 eching

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

x uchun yechish

$$x<\frac{1}{5}$$

Yechim qadamlari

Tenglamaning ikkala tarafini 6 ga, 2,3 ning eng kichik karralisiga ko‘paytiring. 6 >0 bo‘lganda, tengsizlikning yo‘nalishi o‘zgarmasdan qoladi.

$$6-3\left(x+3\right)>2\left(x-2\right)$$

-3 ga x+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6-3x-9>2\left(x-2\right)$$

-3 olish uchun 6 dan 9 ni ayirish.

$$-3-3x>2\left(x-2\right)$$

2 ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-3-3x>2x-4$$

Ikkala tarafdan 2x ni ayirish.

$$-3-3x-2x>-4$$

-5x ni olish uchun -3x va -2x ni birlashtirish.

$$-3-5x>-4$$

3 ni ikki tarafga qo’shing.

$$-5x>-4+3$$

-1 olish uchun -4 va 3'ni qo'shing.

$$-5x>-1$$

Ikki tarafini -5 ga bo‘ling. -5 <0 bo‘lganda, tengsizlikning yo‘nalishi o‘zgargan bo‘ladi.

$$x<\frac{-1}{-5}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-1}{-5} kasrini \frac{1}{5} ga soddalashtirish mumkin.

$$x<\frac{1}{5}$$