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

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

x uchun yechish

$$x\leq \frac{9}{2}$$

Yechim qadamlari

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

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

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

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

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

$$\frac{15}{6}+\frac{5}{6}\left(-1\right)x-\frac{1}{2}\left(x-4\right)\geq \frac{1}{2}\left(2x-3\right)-x$$

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

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

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

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

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

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

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

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

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

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

2 ni olish uchun 4 ni 2 ga bo‘ling.

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

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

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

2 ni \frac{4}{2} kasrga o‘giring.

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

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

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

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

$$\frac{9}{2}-\frac{4}{3}x\geq \frac{1}{2}\left(2x-3\right)-x$$

\frac{1}{2} ga 2x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{9}{2}-\frac{4}{3}x\geq \frac{1}{2}\times 2x+\frac{1}{2}\left(-3\right)-x$$

2 va 2 ni qisqartiring.

$$\frac{9}{2}-\frac{4}{3}x\geq x+\frac{1}{2}\left(-3\right)-x$$

\frac{-3}{2} hosil qilish uchun \frac{1}{2} va -3 ni ko'paytirish.

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

\frac{-3}{2} kasri manfiy belgini olib tashlash bilan -\frac{3}{2} sifatida qayta yozilishi mumkin.

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

0 ni olish uchun x va -x ni birlashtirish.

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

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

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

-\frac{3}{2} va \frac{9}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

-12 olish uchun -3 dan 9 ni ayirish.

$$-\frac{4}{3}x\geq \frac{-12}{2}$$

-6 ni olish uchun -12 ni 2 ga bo‘ling.

$$-\frac{4}{3}x\geq -6$$

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.

$$x\leq -6\left(-\frac{3}{4}\right)$$

-6\left(-\frac{3}{4}\right) ni yagona kasrga aylantiring.

$$x\leq \frac{-6\left(-3\right)}{4}$$

18 hosil qilish uchun -6 va -3 ni ko'paytirish.

$$x\leq \frac{18}{4}$$

\frac{18}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x\leq \frac{9}{2}$$