(2+4/5):(7-7/5)=5^2/2^3*2^2:x eching

$$( 2 + \frac { 4 } { 5 } ) : ( 7 - \frac { 7 } { 5 } ) = \frac { 5 ^ { 2 } } { 2 ^ { 3 } \cdot 2 ^ { 2 } } : x$$

x uchun yechish

$$x = \frac{25}{16} = 1\frac{9}{16} = 1,5625$$

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.

$$\frac{5}{28}x\left(2+\frac{4}{5}\right)=\frac{5^{2}}{2^{3}\times 2^{2}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 2 ni qo‘shib, 5 ni oling.

$$\frac{5}{28}x\left(2+\frac{4}{5}\right)=\frac{5^{2}}{2^{5}}$$

2 ni \frac{10}{5} kasrga o‘giring.

$$\frac{5}{28}x\left(\frac{10}{5}+\frac{4}{5}\right)=\frac{5^{2}}{2^{5}}$$

\frac{10}{5} va \frac{4}{5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{5}{28}x\times \frac{10+4}{5}=\frac{5^{2}}{2^{5}}$$

14 olish uchun 10 va 4'ni qo'shing.

$$\frac{5}{28}x\times \frac{14}{5}=\frac{5^{2}}{2^{5}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{28} ni \frac{14}{5} ga ko‘paytiring.

$$\frac{5\times 14}{28\times 5}x=\frac{5^{2}}{2^{5}}$$

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\frac{14}{28}x=\frac{5^{2}}{2^{5}}$$

\frac{14}{28} ulushini 14 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}x=\frac{5^{2}}{2^{5}}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{1}{2}x=\frac{25}{2^{5}}$$

5 daraja ko‘rsatkichini 2 ga hisoblang va 32 ni qiymatni oling.

$$\frac{1}{2}x=\frac{25}{32}$$

Ikki tarafini 2 va teskari kasri \frac{1}{2} ga ko‘paytiring.

$$x=\frac{25}{32}\times 2$$

\frac{25}{32}\times 2 ni yagona kasrga aylantiring.

$$x=\frac{25\times 2}{32}$$

50 hosil qilish uchun 25 va 2 ni ko'paytirish.

$$x=\frac{50}{32}$$

\frac{50}{32} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{25}{16}$$