2left(1*5x-2*1right)+1*7geq2left(2*4x-3*5right) eching

$$2 \left( 1 \cdot 5x-2 \cdot 1 \right) +1 \cdot 7 \geq 2 \left( 2 \cdot 4x-3 \cdot 5 \right)$$

x uchun yechish

$$x\leq \frac{11}{2}$$

Yechim qadamlari

5 hosil qilish uchun 1 va 5 ni ko'paytirish.

$$2\left(5x-2\times 1\right)+1\times 7\geq 2\left(2\times 4x-3\times 5\right)$$

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

$$2\left(5x-2\right)+1\times 7\geq 2\left(2\times 4x-3\times 5\right)$$

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

$$10x-4+1\times 7\geq 2\left(2\times 4x-3\times 5\right)$$

7 hosil qilish uchun 1 va 7 ni ko'paytirish.

$$10x-4+7\geq 2\left(2\times 4x-3\times 5\right)$$

3 olish uchun -4 va 7'ni qo'shing.

$$10x+3\geq 2\left(2\times 4x-3\times 5\right)$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$10x+3\geq 2\left(8x-3\times 5\right)$$

15 hosil qilish uchun 3 va 5 ni ko'paytirish.

$$10x+3\geq 2\left(8x-15\right)$$

2 ga 8x-15 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$10x+3\geq 16x-30$$

Ikkala tarafdan 16x ni ayirish.

$$10x+3-16x\geq -30$$

-6x ni olish uchun 10x va -16x ni birlashtirish.

$$-6x+3\geq -30$$

Ikkala tarafdan 3 ni ayirish.

$$-6x\geq -30-3$$

-33 olish uchun -30 dan 3 ni ayirish.

$$-6x\geq -33$$

Ikki tarafini -6 ga bo‘ling. -6 manfiy boʻlgani uchun tengsizlikning yo‘nalishi o‘zgaradi.

$$x\leq \frac{-33}{-6}$$

\frac{-33}{-6} ulushini -3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x\leq \frac{11}{2}$$