2/3(x+7)-x/4leq1/2(3-x)+x/6 eching

$$\frac{ 2 }{ 3 } (x+7)- \frac{ x }{ 4 } \leq \frac{ 1 }{ 2 } (3-x)+ \frac{ x }{ 6 }$$

x uchun yechish

$$x\leq -\frac{38}{9}$$

Yechim qadamlari

Tenglamaning ikkala tarafini 12 ga, 3,4,2,6 ning eng kichik karralisiga ko‘paytiring. 12 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$8\left(x+7\right)-3x\leq 6\left(3-x\right)+2x$$

8 ga x+7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8x+56-3x\leq 6\left(3-x\right)+2x$$

5x ni olish uchun 8x va -3x ni birlashtirish.

$$5x+56\leq 6\left(3-x\right)+2x$$

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

$$5x+56\leq 18-6x+2x$$

-4x ni olish uchun -6x va 2x ni birlashtirish.

$$5x+56\leq 18-4x$$

4x ni ikki tarafga qo’shing.

$$5x+56+4x\leq 18$$

9x ni olish uchun 5x va 4x ni birlashtirish.

$$9x+56\leq 18$$

Ikkala tarafdan 56 ni ayirish.

$$9x\leq 18-56$$

-38 olish uchun 18 dan 56 ni ayirish.

$$9x\leq -38$$

Ikki tarafini 9 ga bo‘ling. 9 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$x\leq -\frac{38}{9}$$