5(x/5+10/2)geq2x+30/5 eching

$$5 ( \frac { x } { 5 } + \frac { 10 } { 2 } ) \geq 2 x + \frac { 30 } { 5 }$$

x uchun yechish

$$x\leq 19$$

Yechim qadamlari

Tenglamaning ikkala tarafini 10 ga, 5,2 ning eng kichik karralisiga ko‘paytiring. 10 >0 bo‘lganda, tengsizlikning yo‘nalishi o‘zgarmasdan qoladi.

$$50\left(\frac{x}{5}+\frac{10}{2}\right)\geq 20x+2\times 30$$

5 ni olish uchun 10 ni 2 ga bo‘ling.

$$50\left(\frac{x}{5}+5\right)\geq 20x+2\times 30$$

50 ga \frac{x}{5}+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$50\times \frac{x}{5}+250\geq 20x+2\times 30$$

50 va 5 ichida eng katta umumiy 5 faktorini bekor qiling.

$$10x+250\geq 20x+2\times 30$$

60 hosil qilish uchun 2 va 30 ni ko'paytirish.

$$10x+250\geq 20x+60$$

Ikkala tarafdan 20x ni ayirish.

$$10x+250-20x\geq 60$$

-10x ni olish uchun 10x va -20x ni birlashtirish.

$$-10x+250\geq 60$$

Ikkala tarafdan 250 ni ayirish.

$$-10x\geq 60-250$$

-190 olish uchun 60 dan 250 ni ayirish.

$$-10x\geq -190$$

Ikki tarafini -10 ga bo‘ling. -10 <0 bo‘lganda, tengsizlikning yo‘nalishi o‘zgargan bo‘ladi.

$$x\leq \frac{-190}{-10}$$

19 ni olish uchun -190 ni -10 ga bo‘ling.

$$x\leq 19$$