75%(x-1)-25%(x-4)=25%(x+6) eching

$$75 \% ( x - 1 ) - 25 \% ( x - 4 ) = 25 \% ( x + 6 )$$

x uchun yechish

$$x=5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{75}{100} ulushini 25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{3}{4}\left(x-1\right)-\frac{25}{100}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

\frac{3}{4} ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{4}x+\frac{3}{4}\left(-1\right)-\frac{25}{100}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

-\frac{3}{4} hosil qilish uchun \frac{3}{4} va -1 ni ko'paytirish.

$$\frac{3}{4}x-\frac{3}{4}-\frac{25}{100}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

\frac{25}{100} ulushini 25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

-\frac{1}{4} ga x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x-\frac{1}{4}\left(-4\right)=\frac{25}{100}\left(x+6\right)$$

-\frac{1}{4}\left(-4\right) ni yagona kasrga aylantiring.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x+\frac{-\left(-4\right)}{4}=\frac{25}{100}\left(x+6\right)$$

4 hosil qilish uchun -1 va -4 ni ko'paytirish.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x+\frac{4}{4}=\frac{25}{100}\left(x+6\right)$$

1 ni olish uchun 4 ni 4 ga bo‘ling.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x+1=\frac{25}{100}\left(x+6\right)$$

\frac{1}{2}x ni olish uchun \frac{3}{4}x va -\frac{1}{4}x ni birlashtirish.

$$\frac{1}{2}x-\frac{3}{4}+1=\frac{25}{100}\left(x+6\right)$$

1 ni \frac{4}{4} kasrga o‘giring.

$$\frac{1}{2}x-\frac{3}{4}+\frac{4}{4}=\frac{25}{100}\left(x+6\right)$$

-\frac{3}{4} va \frac{4}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{2}x+\frac{-3+4}{4}=\frac{25}{100}\left(x+6\right)$$

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

$$\frac{1}{2}x+\frac{1}{4}=\frac{25}{100}\left(x+6\right)$$

\frac{25}{100} ulushini 25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

\frac{1}{4} ga x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

\frac{6}{4} hosil qilish uchun \frac{1}{4} va 6 ni ko'paytirish.

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

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

$$\frac{1}{2}x+\frac{1}{4}=\frac{1}{4}x+\frac{3}{2}$$

Ikkala tarafdan \frac{1}{4}x ni ayirish.

$$\frac{1}{2}x+\frac{1}{4}-\frac{1}{4}x=\frac{3}{2}$$

\frac{1}{4}x ni olish uchun \frac{1}{2}x va -\frac{1}{4}x ni birlashtirish.

$$\frac{1}{4}x+\frac{1}{4}=\frac{3}{2}$$

Ikkala tarafdan \frac{1}{4} ni ayirish.

$$\frac{1}{4}x=\frac{3}{2}-\frac{1}{4}$$

2 va 4 ning eng kichik umumiy karralisi 4 ga teng. \frac{3}{2} va \frac{1}{4} ni 4 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1}{4}x=\frac{6}{4}-\frac{1}{4}$$

\frac{6}{4} va \frac{1}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{1}{4}x=\frac{6-1}{4}$$

5 olish uchun 6 dan 1 ni ayirish.

$$\frac{1}{4}x=\frac{5}{4}$$

Ikki tarafini 4 va teskari kasri \frac{1}{4} ga ko‘paytiring.

$$x=\frac{5}{4}\times 4$$

4 va 4 ni qisqartiring.

$$x=5$$