7-9y/2+14leq6y-10/3-19y eching

$$\frac { 7 - 9 y } { 2 } + 14 \leq \frac { 6 y - 10 } { 3 } - 19 y$$

y uchun yechish

$$y\leq -\frac{5}{3}$$

Yechim qadamlari

Tenglamaning ikkala tarafini 6 ga, 2,3 ning eng kichik karralisiga ko‘paytiring. 6 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$3\left(7-9y\right)+84\leq 2\left(6y-10\right)-114y$$

3 ga 7-9y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$21-27y+84\leq 2\left(6y-10\right)-114y$$

105 olish uchun 21 va 84'ni qo'shing.

$$105-27y\leq 2\left(6y-10\right)-114y$$

2 ga 6y-10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$105-27y\leq 12y-20-114y$$

-102y ni olish uchun 12y va -114y ni birlashtirish.

$$105-27y\leq -102y-20$$

102y ni ikki tarafga qo’shing.

$$105-27y+102y\leq -20$$

75y ni olish uchun -27y va 102y ni birlashtirish.

$$105+75y\leq -20$$

Ikkala tarafdan 105 ni ayirish.

$$75y\leq -20-105$$

-125 olish uchun -20 dan 105 ni ayirish.

$$75y\leq -125$$

Ikki tarafini 75 ga bo‘ling. 75 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$y\leq \frac{-125}{75}$$

\frac{-125}{75} ulushini 25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$y\leq -\frac{5}{3}$$