(x-160)*200+(x-170)*400/100000geq02 eching

$$\frac { ( x - 160 ) \times 200 + ( x - 170 ) \times 400 } { 100000 } \geq 02$$

x uchun yechish

$$x\geq \frac{500}{3}$$

Yechim qadamlari

Tenglamaning ikkala tarafini 100000 ga ko'paytirish. 100000 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$\left(x-160\right)\times 200+\left(x-170\right)\times 400\geq 0\times 2$$

x-160 ga 200 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$200x-32000+\left(x-170\right)\times 400\geq 0\times 2$$

x-170 ga 400 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$200x-32000+400x-68000\geq 0\times 2$$

600x ni olish uchun 200x va 400x ni birlashtirish.

$$600x-32000-68000\geq 0\times 2$$

-100000 olish uchun -32000 dan 68000 ni ayirish.

$$600x-100000\geq 0\times 2$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$600x-100000\geq 0$$

100000 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$600x\geq 100000$$

Ikki tarafini 600 ga bo‘ling. 600 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$x\geq \frac{100000}{600}$$

\frac{100000}{600} ulushini 200 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x\geq \frac{500}{3}$$