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

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

x uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

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

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

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

1+x teskarisini topish uchun har birining teskarisini toping.

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

-4 olish uchun -3 dan 1 ni ayirish.

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

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

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

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

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

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

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

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

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

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

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

\frac{7}{6}x ni olish uchun \frac{1}{2}x va \frac{2}{3}x ni birlashtirish.

$$\frac{7}{6}x-4+\frac{1}{6}=\frac{1}{2}x+1$$

-4 ni -\frac{24}{6} kasrga o‘giring.

$$\frac{7}{6}x-\frac{24}{6}+\frac{1}{6}=\frac{1}{2}x+1$$

-\frac{24}{6} va \frac{1}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{7}{6}x+\frac{-24+1}{6}=\frac{1}{2}x+1$$

-23 olish uchun -24 va 1'ni qo'shing.

$$\frac{7}{6}x-\frac{23}{6}=\frac{1}{2}x+1$$

Ikkala tarafdan \frac{1}{2}x ni ayirish.

$$\frac{7}{6}x-\frac{23}{6}-\frac{1}{2}x=1$$

\frac{2}{3}x ni olish uchun \frac{7}{6}x va -\frac{1}{2}x ni birlashtirish.

$$\frac{2}{3}x-\frac{23}{6}=1$$

\frac{23}{6} ni ikki tarafga qo’shing.

$$\frac{2}{3}x=1+\frac{23}{6}$$

1 ni \frac{6}{6} kasrga o‘giring.

$$\frac{2}{3}x=\frac{6}{6}+\frac{23}{6}$$

\frac{6}{6} va \frac{23}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2}{3}x=\frac{6+23}{6}$$

29 olish uchun 6 va 23'ni qo'shing.

$$\frac{2}{3}x=\frac{29}{6}$$

Ikki tarafini \frac{3}{2} va teskari kasri \frac{2}{3} ga ko‘paytiring.

$$x=\frac{29}{6}\times \frac{3}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{29}{6} ni \frac{3}{2} ga ko‘paytiring.

$$x=\frac{29\times 3}{6\times 2}$$

\frac{29\times 3}{6\times 2} kasridagi ko‘paytirishlarni bajaring.

$$x=\frac{87}{12}$$

\frac{87}{12} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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