x-1/4-x-1/3geq2+1-2x/6 eching

$$\frac { x - 1 } { 4 } - \frac { x - 1 } { 3 } \geq 2 + \frac { 1 - 2 x } { 6 }$$

x uchun yechish

$$x\geq \frac{25}{3}$$

Yechim qadamlari

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

$$3\left(x-1\right)-4\left(x-1\right)\geq 24+2\left(1-2x\right)$$

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

$$3x-3-4\left(x-1\right)\geq 24+2\left(1-2x\right)$$

-4 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x-3-4x+4\geq 24+2\left(1-2x\right)$$

-x ni olish uchun 3x va -4x ni birlashtirish.

$$-x-3+4\geq 24+2\left(1-2x\right)$$

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

$$-x+1\geq 24+2\left(1-2x\right)$$

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

$$-x+1\geq 24+2-4x$$

26 olish uchun 24 va 2'ni qo'shing.

$$-x+1\geq 26-4x$$

4x ni ikki tarafga qo’shing.

$$-x+1+4x\geq 26$$

3x ni olish uchun -x va 4x ni birlashtirish.

$$3x+1\geq 26$$

Ikkala tarafdan 1 ni ayirish.

$$3x\geq 26-1$$

25 olish uchun 26 dan 1 ni ayirish.

$$3x\geq 25$$

Ikki tarafini 3 ga bo‘ling. 3 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$x\geq \frac{25}{3}$$