n+3/2-1leq3n/4+5/6 eching

$$\frac { n + 3 } { 2 } - 1 \leq \frac { 3 n } { 4 } + \frac { 5 } { 6 }$$

n uchun yechish

$$n\geq -\frac{4}{3}$$

Yechim qadamlari

Tenglamaning ikkala tarafini 12 ga, 2,4,6 ning eng kichik karralisiga ko‘paytiring. 12 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$6\left(n+3\right)-12\leq 3\times 3n+10$$

6 ga n+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6n+18-12\leq 3\times 3n+10$$

6 olish uchun 18 dan 12 ni ayirish.

$$6n+6\leq 3\times 3n+10$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$6n+6\leq 9n+10$$

Ikkala tarafdan 9n ni ayirish.

$$6n+6-9n\leq 10$$

-3n ni olish uchun 6n va -9n ni birlashtirish.

$$-3n+6\leq 10$$

Ikkala tarafdan 6 ni ayirish.

$$-3n\leq 10-6$$

4 olish uchun 10 dan 6 ni ayirish.

$$-3n\leq 4$$

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

$$n\geq -\frac{4}{3}$$