2(x+1)-(7x+5/7-2)<0 eching

$$2 ( x + 1 ) - ( \frac { 7 x + 5 } { 7 } - 2 ) < 0$$

x uchun yechish

$$x<-\frac{23}{7}$$

Yechim qadamlari

Tenglamaning ikkala tarafini 7 ga ko'paytirish. 7 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$14\left(x+1\right)-7\left(\frac{7x+5}{7}-2\right)<0$$

14 ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$14x+14-7\left(\frac{7x+5}{7}-2\right)<0$$

x+\frac{5}{7} natijani olish uchun 7x+5 ning har bir ifodasini 7 ga bo‘ling.

$$14x+14-7\left(x+\frac{5}{7}-2\right)<0$$

2 ni \frac{14}{7} kasrga o‘giring.

$$14x+14-7\left(x+\frac{5}{7}-\frac{14}{7}\right)<0$$

\frac{5}{7} va \frac{14}{7} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$14x+14-7\left(x+\frac{5-14}{7}\right)<0$$

-9 olish uchun 5 dan 14 ni ayirish.

$$14x+14-7\left(x-\frac{9}{7}\right)<0$$

-7 ga x-\frac{9}{7} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$14x+14-7x-7\left(-\frac{9}{7}\right)<0$$

-7 ni -\frac{9}{7} marotabaga ko'paytirish.

$$14x+14-7x+9<0$$

7x ni olish uchun 14x va -7x ni birlashtirish.

$$7x+14+9<0$$

23 olish uchun 14 va 9'ni qo'shing.

$$7x+23<0$$

Ikkala tarafdan 23 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$7x<-23$$

Ikki tarafini 7 ga bo‘ling. 7 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$x<-\frac{23}{7}$$