x+3/2-1leq3x/4+5/6 eching

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

x uchun yechish

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

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.

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

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

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

6 olish uchun 18 dan 12 ni ayirish.

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

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

$$6x+6\leq 9x+10$$

Ikkala tarafdan 9x ni ayirish.

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

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

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

Ikkala tarafdan 6 ni ayirish.

$$-3x\leq 10-6$$

4 olish uchun 10 dan 6 ni ayirish.

$$-3x\leq 4$$

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

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