2(3/2x-21/10)+17/10geq2(12/5x-frac{7}{2}) eching

$$2 ( \frac { 3 } { 2 } x - \frac { 21 } { 10 } ) + \frac { 17 } { 10 } \geq 2 ( \frac { 12 } { 5 } x - \frac { 7 } { 2 } )$$

x uchun yechish

$$x\leq \frac{5}{2}$$

Yechim qadamlari

2 ga \frac{3}{2}x-\frac{21}{10} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2\times \frac{3}{2}x+2\left(-\frac{21}{10}\right)+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

2 va 2 ni qisqartiring.

$$3x+2\left(-\frac{21}{10}\right)+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

2\left(-\frac{21}{10}\right) ni yagona kasrga aylantiring.

$$3x+\frac{2\left(-21\right)}{10}+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

-42 hosil qilish uchun 2 va -21 ni ko'paytirish.

$$3x+\frac{-42}{10}+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

\frac{-42}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$3x-\frac{21}{5}+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

5 va 10 ning eng kichik umumiy karralisi 10 ga teng. -\frac{21}{5} va \frac{17}{10} ni 10 maxraj bilan kasrlarga aylantirib oling.

$$3x-\frac{42}{10}+\frac{17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

-\frac{42}{10} va \frac{17}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$3x+\frac{-42+17}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

-25 olish uchun -42 va 17'ni qo'shing.

$$3x+\frac{-25}{10}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

\frac{-25}{10} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$3x-\frac{5}{2}\geq 2\left(\frac{12}{5}x-\frac{7}{2}\right)$$

2 ga \frac{12}{5}x-\frac{7}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x-\frac{5}{2}\geq 2\times \frac{12}{5}x+2\left(-\frac{7}{2}\right)$$

2\times \frac{12}{5} ni yagona kasrga aylantiring.

$$3x-\frac{5}{2}\geq \frac{2\times 12}{5}x+2\left(-\frac{7}{2}\right)$$

24 hosil qilish uchun 2 va 12 ni ko'paytirish.

$$3x-\frac{5}{2}\geq \frac{24}{5}x+2\left(-\frac{7}{2}\right)$$

2 va 2 ni qisqartiring.

$$3x-\frac{5}{2}\geq \frac{24}{5}x-7$$

Ikkala tarafdan \frac{24}{5}x ni ayirish.

$$3x-\frac{5}{2}-\frac{24}{5}x\geq -7$$

-\frac{9}{5}x ni olish uchun 3x va -\frac{24}{5}x ni birlashtirish.

$$-\frac{9}{5}x-\frac{5}{2}\geq -7$$

\frac{5}{2} ni ikki tarafga qo’shing.

$$-\frac{9}{5}x\geq -7+\frac{5}{2}$$

-7 ni -\frac{14}{2} kasrga o‘giring.

$$-\frac{9}{5}x\geq -\frac{14}{2}+\frac{5}{2}$$

-\frac{14}{2} va \frac{5}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$-\frac{9}{5}x\geq \frac{-14+5}{2}$$

-9 olish uchun -14 va 5'ni qo'shing.

$$-\frac{9}{5}x\geq -\frac{9}{2}$$

Ikki tarafini -\frac{5}{9} va teskari kasri -\frac{9}{5} ga ko‘paytiring. -\frac{9}{5} manfiy boʻlgani uchun tengsizlikning yo‘nalishi o‘zgaradi.

$$x\leq -\frac{9}{2}\left(-\frac{5}{9}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{9}{2} ni -\frac{5}{9} ga ko‘paytiring.

$$x\leq \frac{-9\left(-5\right)}{2\times 9}$$

\frac{-9\left(-5\right)}{2\times 9} kasridagi ko‘paytirishlarni bajaring.

$$x\leq \frac{45}{18}$$

\frac{45}{18} ulushini 9 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x\leq \frac{5}{2}$$