3/5x-[7/4(x/5+1/2)]=frac{7}{3}y-frac{5}{4} eching

$$\frac { 3 } { 5 } x - [ \frac { 7 } { 4 } ( \frac { x } { 5 } + \frac { 1 } { 2 } ) ] = \frac { 7 } { 3 } y - \frac { 5 } { 4 }$$

x uchun yechish

$$x=\frac{28y}{3}-\frac{3}{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 60 ga, 5,4,2,3 ning eng kichik karralisiga ko‘paytiring.

$$36x-105\left(\frac{x}{5}+\frac{1}{2}\right)=140y-75$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 va 2 ning eng kichik umumiy karralisi 10. \frac{x}{5} ni \frac{2}{2} marotabaga ko'paytirish. \frac{1}{2} ni \frac{5}{5} marotabaga ko'paytirish.

$$36x-105\left(\frac{2x}{10}+\frac{5}{10}\right)=140y-75$$

\frac{2x}{10} va \frac{5}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$36x-105\times \frac{2x+5}{10}=140y-75$$

105\times \frac{2x+5}{10} ni yagona kasrga aylantiring.

$$36x-\frac{105\left(2x+5\right)}{10}=140y-75$$

105 ga 2x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$36x-\frac{210x+525}{10}=140y-75$$

21x+\frac{105}{2} natijani olish uchun 210x+525 ning har bir ifodasini 10 ga bo‘ling.

$$36x-\left(21x+\frac{105}{2}\right)=140y-75$$

21x+\frac{105}{2} teskarisini topish uchun har birining teskarisini toping.

$$36x-21x-\frac{105}{2}=140y-75$$

15x ni olish uchun 36x va -21x ni birlashtirish.

$$15x-\frac{105}{2}=140y-75$$

\frac{105}{2} ni ikki tarafga qo’shing.

$$15x=140y-75+\frac{105}{2}$$

-\frac{45}{2} olish uchun -75 va \frac{105}{2}'ni qo'shing.

$$15x=140y-\frac{45}{2}$$

Ikki tarafini 15 ga bo‘ling.

$$\frac{15x}{15}=\frac{140y-\frac{45}{2}}{15}$$

15 ga bo'lish 15 ga ko'paytirishni bekor qiladi.

$$x=\frac{140y-\frac{45}{2}}{15}$$

140y-\frac{45}{2} ni 15 ga bo'lish.

$$x=\frac{28y}{3}-\frac{3}{2}$$

y uchun yechish

$$y=\frac{3x}{28}+\frac{9}{56}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 60 ga, 5,4,2,3 ning eng kichik karralisiga ko‘paytiring.

$$36x-105\left(\frac{x}{5}+\frac{1}{2}\right)=140y-75$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 va 2 ning eng kichik umumiy karralisi 10. \frac{x}{5} ni \frac{2}{2} marotabaga ko'paytirish. \frac{1}{2} ni \frac{5}{5} marotabaga ko'paytirish.

$$36x-105\left(\frac{2x}{10}+\frac{5}{10}\right)=140y-75$$

\frac{2x}{10} va \frac{5}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$36x-105\times \frac{2x+5}{10}=140y-75$$

105\times \frac{2x+5}{10} ni yagona kasrga aylantiring.

$$36x-\frac{105\left(2x+5\right)}{10}=140y-75$$

105 ga 2x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$36x-\frac{210x+525}{10}=140y-75$$

21x+\frac{105}{2} natijani olish uchun 210x+525 ning har bir ifodasini 10 ga bo‘ling.

$$36x-\left(21x+\frac{105}{2}\right)=140y-75$$

21x+\frac{105}{2} teskarisini topish uchun har birining teskarisini toping.

$$36x-21x-\frac{105}{2}=140y-75$$

15x ni olish uchun 36x va -21x ni birlashtirish.

$$15x-\frac{105}{2}=140y-75$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$140y-75=15x-\frac{105}{2}$$

75 ni ikki tarafga qo’shing.

$$140y=15x-\frac{105}{2}+75$$

\frac{45}{2} olish uchun -\frac{105}{2} va 75'ni qo'shing.

$$140y=15x+\frac{45}{2}$$

Ikki tarafini 140 ga bo‘ling.

$$\frac{140y}{140}=\frac{15x+\frac{45}{2}}{140}$$

140 ga bo'lish 140 ga ko'paytirishni bekor qiladi.

$$y=\frac{15x+\frac{45}{2}}{140}$$

15x+\frac{45}{2} ni 140 ga bo'lish.

$$y=\frac{3x}{28}+\frac{9}{56}$$