4(x+2)/3-6(x-7)/7geq12 eching

$$\frac { 4 ( x + 2 ) } { 3 } - \frac { 6 ( x - 7 ) } { 7 } \geq 12$$

x uchun yechish

$$x\geq 7$$

Yechim qadamlari

Tenglamaning ikkala tarafini 21 ga, 3,7 ning eng kichik karralisiga ko‘paytiring. 21 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$7\times 4\left(x+2\right)-3\times 6\left(x-7\right)\geq 252$$

28 hosil qilish uchun 7 va 4 ni ko'paytirish.

$$28\left(x+2\right)-3\times 6\left(x-7\right)\geq 252$$

28 ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$28x+56-3\times 6\left(x-7\right)\geq 252$$

-18 hosil qilish uchun -3 va 6 ni ko'paytirish.

$$28x+56-18\left(x-7\right)\geq 252$$

-18 ga x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$28x+56-18x+126\geq 252$$

10x ni olish uchun 28x va -18x ni birlashtirish.

$$10x+56+126\geq 252$$

182 olish uchun 56 va 126'ni qo'shing.

$$10x+182\geq 252$$

Ikkala tarafdan 182 ni ayirish.

$$10x\geq 252-182$$

70 olish uchun 252 dan 182 ni ayirish.

$$10x\geq 70$$

Ikki tarafini 10 ga bo‘ling. 10 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$x\geq \frac{70}{10}$$

7 ni olish uchun 70 ni 10 ga bo‘ling.

$$x\geq 7$$