1/4(x-2)=1/3(2x+6) eching

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

x uchun yechish

$$x=-6$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{1}{4} ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

\frac{-2}{4} hosil qilish uchun \frac{1}{4} va -2 ni ko'paytirish.

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

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

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

\frac{1}{3} ga 2x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{1}{4}x-\frac{1}{2}=\frac{1}{3}\times 2x+\frac{1}{3}\times 6$$

\frac{2}{3} hosil qilish uchun \frac{1}{3} va 2 ni ko'paytirish.

$$\frac{1}{4}x-\frac{1}{2}=\frac{2}{3}x+\frac{1}{3}\times 6$$

\frac{6}{3} hosil qilish uchun \frac{1}{3} va 6 ni ko'paytirish.

$$\frac{1}{4}x-\frac{1}{2}=\frac{2}{3}x+\frac{6}{3}$$

2 ni olish uchun 6 ni 3 ga bo‘ling.

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

Ikkala tarafdan \frac{2}{3}x ni ayirish.

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

-\frac{5}{12}x ni olish uchun \frac{1}{4}x va -\frac{2}{3}x ni birlashtirish.

$$-\frac{5}{12}x-\frac{1}{2}=2$$

\frac{1}{2} ni ikki tarafga qo’shing.

$$-\frac{5}{12}x=2+\frac{1}{2}$$

2 ni \frac{4}{2} kasrga o‘giring.

$$-\frac{5}{12}x=\frac{4}{2}+\frac{1}{2}$$

\frac{4}{2} va \frac{1}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$-\frac{5}{12}x=\frac{4+1}{2}$$

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

$$-\frac{5}{12}x=\frac{5}{2}$$

Ikki tarafini -\frac{12}{5} va teskari kasri -\frac{5}{12} ga ko‘paytiring.

$$x=\frac{5}{2}\left(-\frac{12}{5}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{2} ni -\frac{12}{5} ga ko‘paytiring.

$$x=\frac{5\left(-12\right)}{2\times 5}$$

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$x=\frac{-12}{2}$$

-6 ni olish uchun -12 ni 2 ga bo‘ling.

$$x=-6$$