3/4[4/3(1/2x-1/4)-8]=frac{3}{2}x+1 eching

$$\frac { 3 } { 4 } [ \frac { 4 } { 3 } ( \frac { 1 } { 2 } x - \frac { 1 } { 4 } ) - 8 ] = \frac { 3 } { 2 } x + 1$$

x uchun yechish

$$x = -\frac{29}{4} = -7\frac{1}{4} = -7,25$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{4}{3} ga \frac{1}{2}x-\frac{1}{4} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3}{4}\left(\frac{4}{3}\times \frac{1}{2}x+\frac{4}{3}\left(-\frac{1}{4}\right)-8\right)=\frac{3}{2}x+1$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{4}{3} ni \frac{1}{2} ga ko‘paytiring.

$$\frac{3}{4}\left(\frac{4\times 1}{3\times 2}x+\frac{4}{3}\left(-\frac{1}{4}\right)-8\right)=\frac{3}{2}x+1$$

\frac{4\times 1}{3\times 2} kasridagi ko‘paytirishlarni bajaring.

$$\frac{3}{4}\left(\frac{4}{6}x+\frac{4}{3}\left(-\frac{1}{4}\right)-8\right)=\frac{3}{2}x+1$$

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

$$\frac{3}{4}\left(\frac{2}{3}x+\frac{4}{3}\left(-\frac{1}{4}\right)-8\right)=\frac{3}{2}x+1$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{4}{3} ni -\frac{1}{4} ga ko‘paytiring.

$$\frac{3}{4}\left(\frac{2}{3}x+\frac{4\left(-1\right)}{3\times 4}-8\right)=\frac{3}{2}x+1$$

Surat va maxrajdagi ikkala 4 ni qisqartiring.

$$\frac{3}{4}\left(\frac{2}{3}x+\frac{-1}{3}-8\right)=\frac{3}{2}x+1$$

\frac{-1}{3} kasri manfiy belgini olib tashlash bilan -\frac{1}{3} sifatida qayta yozilishi mumkin.

$$\frac{3}{4}\left(\frac{2}{3}x-\frac{1}{3}-8\right)=\frac{3}{2}x+1$$

8 ni \frac{24}{3} kasrga o‘giring.

$$\frac{3}{4}\left(\frac{2}{3}x-\frac{1}{3}-\frac{24}{3}\right)=\frac{3}{2}x+1$$

-\frac{1}{3} va \frac{24}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{3}{4}\left(\frac{2}{3}x+\frac{-1-24}{3}\right)=\frac{3}{2}x+1$$

-25 olish uchun -1 dan 24 ni ayirish.

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

\frac{3}{4} ga \frac{2}{3}x-\frac{25}{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{4} ni \frac{2}{3} ga ko‘paytiring.

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

Surat va maxrajdagi ikkala 3 ni qisqartiring.

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

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

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{4} ni -\frac{25}{3} ga ko‘paytiring.

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

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{1}{2}x+\frac{-25}{4}=\frac{3}{2}x+1$$

\frac{-25}{4} kasri manfiy belgini olib tashlash bilan -\frac{25}{4} sifatida qayta yozilishi mumkin.

$$\frac{1}{2}x-\frac{25}{4}=\frac{3}{2}x+1$$

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

$$\frac{1}{2}x-\frac{25}{4}-\frac{3}{2}x=1$$

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

$$-x-\frac{25}{4}=1$$

\frac{25}{4} ni ikki tarafga qo’shing.

$$-x=1+\frac{25}{4}$$

1 ni \frac{4}{4} kasrga o‘giring.

$$-x=\frac{4}{4}+\frac{25}{4}$$

\frac{4}{4} va \frac{25}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$-x=\frac{4+25}{4}$$

29 olish uchun 4 va 25'ni qo'shing.

$$-x=\frac{29}{4}$$

Ikkala tarafini -1 ga ko‘paytiring.

$$x=-\frac{29}{4}$$