-1/3(5x-21)geq3/4(10-2x) eching

$$- \frac { 1 } { 3 } ( 5 x - 21 ) \geq \frac { 3 } { 4 } ( 10 - 2 x )$$

x uchun yechish

$$x\leq -3$$

Yechim qadamlari

-\frac{1}{3} ga 5x-21 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-\frac{1}{3}\times 5x-\frac{1}{3}\left(-21\right)\geq \frac{3}{4}\left(10-2x\right)$$

-\frac{1}{3}\times 5 ni yagona kasrga aylantiring.

$$\frac{-5}{3}x-\frac{1}{3}\left(-21\right)\geq \frac{3}{4}\left(10-2x\right)$$

\frac{-5}{3} kasri manfiy belgini olib tashlash bilan -\frac{5}{3} sifatida qayta yozilishi mumkin.

$$-\frac{5}{3}x-\frac{1}{3}\left(-21\right)\geq \frac{3}{4}\left(10-2x\right)$$

-\frac{1}{3}\left(-21\right) ni yagona kasrga aylantiring.

$$-\frac{5}{3}x+\frac{-\left(-21\right)}{3}\geq \frac{3}{4}\left(10-2x\right)$$

21 hosil qilish uchun -1 va -21 ni ko'paytirish.

$$-\frac{5}{3}x+\frac{21}{3}\geq \frac{3}{4}\left(10-2x\right)$$

7 ni olish uchun 21 ni 3 ga bo‘ling.

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

\frac{3}{4} ga 10-2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

\frac{3}{4}\times 10 ni yagona kasrga aylantiring.

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

30 hosil qilish uchun 3 va 10 ni ko'paytirish.

$$-\frac{5}{3}x+7\geq \frac{30}{4}+\frac{3}{4}\left(-2\right)x$$

\frac{30}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{5}{3}x+7\geq \frac{15}{2}+\frac{3}{4}\left(-2\right)x$$

\frac{3}{4}\left(-2\right) ni yagona kasrga aylantiring.

$$-\frac{5}{3}x+7\geq \frac{15}{2}+\frac{3\left(-2\right)}{4}x$$

-6 hosil qilish uchun 3 va -2 ni ko'paytirish.

$$-\frac{5}{3}x+7\geq \frac{15}{2}+\frac{-6}{4}x$$

\frac{-6}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{5}{3}x+7\geq \frac{15}{2}-\frac{3}{2}x$$

\frac{3}{2}x ni ikki tarafga qo’shing.

$$-\frac{5}{3}x+7+\frac{3}{2}x\geq \frac{15}{2}$$

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

$$-\frac{1}{6}x+7\geq \frac{15}{2}$$

Ikkala tarafdan 7 ni ayirish.

$$-\frac{1}{6}x\geq \frac{15}{2}-7$$

7 ni \frac{14}{2} kasrga o‘giring.

$$-\frac{1}{6}x\geq \frac{15}{2}-\frac{14}{2}$$

\frac{15}{2} va \frac{14}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$-\frac{1}{6}x\geq \frac{15-14}{2}$$

1 olish uchun 15 dan 14 ni ayirish.

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

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

$$x\leq \frac{1}{2}\left(-6\right)$$

\frac{-6}{2} hosil qilish uchun \frac{1}{2} va -6 ni ko'paytirish.

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

-3 ni olish uchun -6 ni 2 ga bo‘ling.

$$x\leq -3$$