5(2-3x)+4(3x+5)leq2(-x+1) eching

$$5 ( 2 - 3 x ) + 4 ( 3 x + 5 ) \leq 2 ( - x + 1 )$$

x uchun yechish

$$x\geq 28$$

Yechim qadamlari

5 ga 2-3x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$10-15x+4\left(3x+5\right)\leq 2\left(-x+1\right)$$

4 ga 3x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$10-15x+12x+20\leq 2\left(-x+1\right)$$

-3x ni olish uchun -15x va 12x ni birlashtirish.

$$10-3x+20\leq 2\left(-x+1\right)$$

30 olish uchun 10 va 20'ni qo'shing.

$$30-3x\leq 2\left(-x+1\right)$$

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

$$30-3x\leq 2\left(-x\right)+2$$

Ikkala tarafdan 2\left(-x\right) ni ayirish.

$$30-3x-2\left(-x\right)\leq 2$$

-2 hosil qilish uchun -1 va 2 ni ko'paytirish.

$$30-3x-2\left(-1\right)x\leq 2$$

2 hosil qilish uchun -2 va -1 ni ko'paytirish.

$$30-3x+2x\leq 2$$

-x ni olish uchun -3x va 2x ni birlashtirish.

$$30-x\leq 2$$

Ikkala tarafdan 30 ni ayirish.

$$-x\leq 2-30$$

-28 olish uchun 2 dan 30 ni ayirish.

$$-x\leq -28$$

Ikki tarafini -1 ga bo‘ling. -1 <0 bo‘lganda, tengsizlikning yo‘nalishi o‘zgargan bo‘ladi.

$$x\geq \frac{-28}{-1}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-28}{-1} kasrini 28 ga soddalashtirish mumkin.

$$x\geq 28$$