1/9(3k-3/2)geq-2(k/2+3) eching

$$\frac { 1 } { 9 } ( 3 k - \frac { 3 } { 2 } ) \geq - 2 ( \frac { k } { 2 } + 3 )$$

k uchun yechish

$$k\geq -\frac{35}{8}$$

Yechim qadamlari

Tenglamaning ikkala tarafini 18 ga, 9,2 ning eng kichik karralisiga ko‘paytiring. 18 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$2\left(3k-\frac{3}{2}\right)\geq -36\left(\frac{k}{2}+3\right)$$

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

$$6k+2\left(-\frac{3}{2}\right)\geq -36\left(\frac{k}{2}+3\right)$$

2 va 2 ni qisqartiring.

$$6k-3\geq -36\left(\frac{k}{2}+3\right)$$

-36 ga \frac{k}{2}+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6k-3\geq -36\times \frac{k}{2}-108$$

36 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

$$6k-3\geq -18k-108$$

18k ni ikki tarafga qo’shing.

$$6k-3+18k\geq -108$$

24k ni olish uchun 6k va 18k ni birlashtirish.

$$24k-3\geq -108$$

3 ni ikki tarafga qo’shing.

$$24k\geq -108+3$$

-105 olish uchun -108 va 3'ni qo'shing.

$$24k\geq -105$$

Ikki tarafini 24 ga bo‘ling. 24 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$k\geq \frac{-105}{24}$$

\frac{-105}{24} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$k\geq -\frac{35}{8}$$