2/3(x+1)-5/6(x-7)leq2 eching

$$\frac { 2 } { 3 } ( x + 1 ) - \frac { 5 } { 6 } ( x - 7 ) \leq 2$$

x uchun yechish

$$x\geq 27$$

Yechim qadamlari

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

$$\frac{2}{3}x+\frac{2}{3}-\frac{5}{6}\left(x-7\right)\leq 2$$

-\frac{5}{6} ga x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{2}{3}x+\frac{2}{3}-\frac{5}{6}x-\frac{5}{6}\left(-7\right)\leq 2$$

-\frac{5}{6}\left(-7\right) ni yagona kasrga aylantiring.

$$\frac{2}{3}x+\frac{2}{3}-\frac{5}{6}x+\frac{-5\left(-7\right)}{6}\leq 2$$

35 hosil qilish uchun -5 va -7 ni ko'paytirish.

$$\frac{2}{3}x+\frac{2}{3}-\frac{5}{6}x+\frac{35}{6}\leq 2$$

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

$$-\frac{1}{6}x+\frac{2}{3}+\frac{35}{6}\leq 2$$

3 va 6 ning eng kichik umumiy karralisi 6 ga teng. \frac{2}{3} va \frac{35}{6} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$-\frac{1}{6}x+\frac{4}{6}+\frac{35}{6}\leq 2$$

\frac{4}{6} va \frac{35}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$-\frac{1}{6}x+\frac{4+35}{6}\leq 2$$

39 olish uchun 4 va 35'ni qo'shing.

$$-\frac{1}{6}x+\frac{39}{6}\leq 2$$

\frac{39}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{1}{6}x+\frac{13}{2}\leq 2$$

Ikkala tarafdan \frac{13}{2} ni ayirish.

$$-\frac{1}{6}x\leq 2-\frac{13}{2}$$

2 ni \frac{4}{2} kasrga o‘giring.

$$-\frac{1}{6}x\leq \frac{4}{2}-\frac{13}{2}$$

\frac{4}{2} va \frac{13}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$-\frac{1}{6}x\leq \frac{4-13}{2}$$

-9 olish uchun 4 dan 13 ni ayirish.

$$-\frac{1}{6}x\leq -\frac{9}{2}$$

Ikki tarafini -6 va teskari kasri -\frac{1}{6} ga ko‘paytiring. -\frac{1}{6} manfiy boʻlgani uchun tengsizlikning yo‘nalishi o‘zgaradi.

$$x\geq -\frac{9}{2}\left(-6\right)$$

-\frac{9}{2}\left(-6\right) ni yagona kasrga aylantiring.

$$x\geq \frac{-9\left(-6\right)}{2}$$

54 hosil qilish uchun -9 va -6 ni ko'paytirish.

$$x\geq \frac{54}{2}$$

27 ni olish uchun 54 ni 2 ga bo‘ling.

$$x\geq 27$$