2x-1/2-5x+2/6-xleq-1 eching

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

x uchun yechish

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

Yechim qadamlari

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

$$3\left(2x-1\right)-\left(5x+2\right)-6x\leq -6$$

3 ga 2x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x-3-\left(5x+2\right)-6x\leq -6$$

5x+2 teskarisini topish uchun har birining teskarisini toping.

$$6x-3-5x-2-6x\leq -6$$

x ni olish uchun 6x va -5x ni birlashtirish.

$$x-3-2-6x\leq -6$$

-5 olish uchun -3 dan 2 ni ayirish.

$$x-5-6x\leq -6$$

-5x ni olish uchun x va -6x ni birlashtirish.

$$-5x-5\leq -6$$

5 ni ikki tarafga qo’shing.

$$-5x\leq -6+5$$

-1 olish uchun -6 va 5'ni qo'shing.

$$-5x\leq -1$$

Ikki tarafini -5 ga bo‘ling. -5 manfiy boʻlgani uchun tengsizlikning yo‘nalishi o‘zgaradi.

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

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

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