5/6(3-x)-1/2(x-4)geq1/2 eching

$$\frac { 5 } { 6 } ( 3 - x ) - \frac { 1 } { 2 } ( x - 4 ) \geq \frac { 1 } { 2 }$$

x uchun yechish

$$x\leq 3$$

Yechim qadamlari

\frac{5}{6} ga 3-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{5}{6}\times 3+\frac{5}{6}\left(-1\right)x-\frac{1}{2}\left(x-4\right)\geq \frac{1}{2}$$

\frac{5}{6}\times 3 ni yagona kasrga aylantiring.

$$\frac{5\times 3}{6}+\frac{5}{6}\left(-1\right)x-\frac{1}{2}\left(x-4\right)\geq \frac{1}{2}$$

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

$$\frac{15}{6}+\frac{5}{6}\left(-1\right)x-\frac{1}{2}\left(x-4\right)\geq \frac{1}{2}$$

\frac{15}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{5}{2}+\frac{5}{6}\left(-1\right)x-\frac{1}{2}\left(x-4\right)\geq \frac{1}{2}$$

-\frac{5}{6} hosil qilish uchun \frac{5}{6} va -1 ni ko'paytirish.

$$\frac{5}{2}-\frac{5}{6}x-\frac{1}{2}\left(x-4\right)\geq \frac{1}{2}$$

-\frac{1}{2} ga x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{5}{2}-\frac{5}{6}x-\frac{1}{2}x-\frac{1}{2}\left(-4\right)\geq \frac{1}{2}$$

-\frac{1}{2}\left(-4\right) ni yagona kasrga aylantiring.

$$\frac{5}{2}-\frac{5}{6}x-\frac{1}{2}x+\frac{-\left(-4\right)}{2}\geq \frac{1}{2}$$

4 hosil qilish uchun -1 va -4 ni ko'paytirish.

$$\frac{5}{2}-\frac{5}{6}x-\frac{1}{2}x+\frac{4}{2}\geq \frac{1}{2}$$

2 ni olish uchun 4 ni 2 ga bo‘ling.

$$\frac{5}{2}-\frac{5}{6}x-\frac{1}{2}x+2\geq \frac{1}{2}$$

-\frac{4}{3}x ni olish uchun -\frac{5}{6}x va -\frac{1}{2}x ni birlashtirish.

$$\frac{5}{2}-\frac{4}{3}x+2\geq \frac{1}{2}$$

2 ni \frac{4}{2} kasrga o‘giring.

$$\frac{5}{2}-\frac{4}{3}x+\frac{4}{2}\geq \frac{1}{2}$$

\frac{5}{2} va \frac{4}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{5+4}{2}-\frac{4}{3}x\geq \frac{1}{2}$$

9 olish uchun 5 va 4'ni qo'shing.

$$\frac{9}{2}-\frac{4}{3}x\geq \frac{1}{2}$$

Ikkala tarafdan \frac{9}{2} ni ayirish.

$$-\frac{4}{3}x\geq \frac{1}{2}-\frac{9}{2}$$

\frac{1}{2} va \frac{9}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$-\frac{4}{3}x\geq \frac{1-9}{2}$$

-8 olish uchun 1 dan 9 ni ayirish.

$$-\frac{4}{3}x\geq \frac{-8}{2}$$

-4 ni olish uchun -8 ni 2 ga bo‘ling.

$$-\frac{4}{3}x\geq -4$$

Ikki tarafini -\frac{3}{4} va teskari kasri -\frac{4}{3} ga ko‘paytiring. -\frac{4}{3} manfiy boʻlgani uchun tengsizlikning yo‘nalishi o‘zgaradi.

$$x\leq -4\left(-\frac{3}{4}\right)$$

-4 ni -\frac{3}{4} marotabaga ko'paytirish.

$$x\leq 3$$