7(17/3-43):x=(5/4*8/10-4/9:2):(frac{5}{4}+frac{2}{5}-frac{1}{4}) eching

$$7 ( \frac { 17 } { 3 } - 43 ) : x = ( \frac { 5 } { 4 } \cdot \frac { 8 } { 10 } - \frac { 4 } { 9 } : 2 ) : ( \frac { 5 } { 4 } + \frac { 2 } { 5 } - \frac { 1 } { 4 } )$$

x uchun yechish

$$x = -\frac{2352}{5} = -470\frac{2}{5} = -470,4$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$7\left(\frac{17}{3}-43\right)=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

43 ni \frac{129}{3} kasrga o‘giring.

$$7\left(\frac{17}{3}-\frac{129}{3}\right)=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

\frac{17}{3} va \frac{129}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$7\times \frac{17-129}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

-112 olish uchun 17 dan 129 ni ayirish.

$$7\left(-\frac{112}{3}\right)=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

7\left(-\frac{112}{3}\right) ni yagona kasrga aylantiring.

$$\frac{7\left(-112\right)}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

-784 hosil qilish uchun 7 va -112 ni ko'paytirish.

$$\frac{-784}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

\frac{-784}{3} kasri manfiy belgini olib tashlash bilan -\frac{784}{3} sifatida qayta yozilishi mumkin.

$$-\frac{784}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

\frac{8}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{784}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{4}{5}-\frac{\frac{4}{9}}{2}\right)$$

\frac{5}{4} va uning teskari kasrini \frac{4}{5} ni qisqartiring.

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{\frac{4}{9}}{2}\right)$$

\frac{\frac{4}{9}}{2} ni yagona kasrga aylantiring.

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{4}{9\times 2}\right)$$

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{4}{18}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{2}{9}\right)$$

1 ni \frac{9}{9} kasrga o‘giring.

$$-\frac{784}{3}=\frac{5}{7}x\left(\frac{9}{9}-\frac{2}{9}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\times \frac{9-2}{9}$$

7 olish uchun 9 dan 2 ni ayirish.

$$-\frac{784}{3}=\frac{5}{7}x\times \frac{7}{9}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{7} ni \frac{7}{9} ga ko‘paytiring.

$$-\frac{784}{3}=\frac{5\times 7}{7\times 9}x$$

Surat va maxrajdagi ikkala 7 ni qisqartiring.

$$-\frac{784}{3}=\frac{5}{9}x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{5}{9}x=-\frac{784}{3}$$

Ikki tarafini \frac{9}{5} va teskari kasri \frac{5}{9} ga ko‘paytiring.

$$x=-\frac{784}{3}\times \frac{9}{5}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{784}{3} ni \frac{9}{5} ga ko‘paytiring.

$$x=\frac{-784\times 9}{3\times 5}$$

\frac{-784\times 9}{3\times 5} kasridagi ko‘paytirishlarni bajaring.

$$x=\frac{-7056}{15}$$

\frac{-7056}{15} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{2352}{5}$$