(2/5+1/10):x=(1/6+1/2+frac{2}{9}):(frac{1}{9}+frac{1}{27}) eching

$$( \frac { 2 } { 5 } + \frac { 1 } { 10 } ) : x = ( \frac { 1 } { 6 } + \frac { 1 } { 2 } + \frac { 2 } { 9 } ) : ( \frac { 1 } { 9 } + \frac { 1 } { 27 } )$$

x uchun yechish

$$x=\frac{1}{12}\approx 0,083333333$$

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.

$$\frac{2}{5}+\frac{1}{10}=\frac{27}{4}x\left(\frac{1}{6}+\frac{1}{2}+\frac{2}{9}\right)$$

5 va 10 ning eng kichik umumiy karralisi 10 ga teng. \frac{2}{5} va \frac{1}{10} ni 10 maxraj bilan kasrlarga aylantirib oling.

$$\frac{4}{10}+\frac{1}{10}=\frac{27}{4}x\left(\frac{1}{6}+\frac{1}{2}+\frac{2}{9}\right)$$

\frac{4}{10} va \frac{1}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{4+1}{10}=\frac{27}{4}x\left(\frac{1}{6}+\frac{1}{2}+\frac{2}{9}\right)$$

5 olish uchun 4 va 1'ni qo'shing.

$$\frac{5}{10}=\frac{27}{4}x\left(\frac{1}{6}+\frac{1}{2}+\frac{2}{9}\right)$$

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

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{1}{6}+\frac{1}{2}+\frac{2}{9}\right)$$

6 va 2 ning eng kichik umumiy karralisi 6 ga teng. \frac{1}{6} va \frac{1}{2} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{1}{6}+\frac{3}{6}+\frac{2}{9}\right)$$

\frac{1}{6} va \frac{3}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{1+3}{6}+\frac{2}{9}\right)$$

4 olish uchun 1 va 3'ni qo'shing.

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{4}{6}+\frac{2}{9}\right)$$

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

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{2}{3}+\frac{2}{9}\right)$$

3 va 9 ning eng kichik umumiy karralisi 9 ga teng. \frac{2}{3} va \frac{2}{9} ni 9 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1}{2}=\frac{27}{4}x\left(\frac{6}{9}+\frac{2}{9}\right)$$

\frac{6}{9} va \frac{2}{9} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{2}=\frac{27}{4}x\times \frac{6+2}{9}$$

8 olish uchun 6 va 2'ni qo'shing.

$$\frac{1}{2}=\frac{27}{4}x\times \frac{8}{9}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{27}{4} ni \frac{8}{9} ga ko‘paytiring.

$$\frac{1}{2}=\frac{27\times 8}{4\times 9}x$$

\frac{27\times 8}{4\times 9} kasridagi ko‘paytirishlarni bajaring.

$$\frac{1}{2}=\frac{216}{36}x$$

6 ni olish uchun 216 ni 36 ga bo‘ling.

$$\frac{1}{2}=6x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$6x=\frac{1}{2}$$

Ikki tarafini 6 ga bo‘ling.

$$x=\frac{\frac{1}{2}}{6}$$

\frac{\frac{1}{2}}{6} ni yagona kasrga aylantiring.

$$x=\frac{1}{2\times 6}$$

12 hosil qilish uchun 2 va 6 ni ko'paytirish.

$$x=\frac{1}{12}$$