2x-(2x-3x-1/8)=2/3(x+2/6)-1/4 eching

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

x uchun yechish

$$x=\frac{7}{19}\approx 0,368421053$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 24 ga, 8,3,6,4 ning eng kichik karralisiga ko‘paytiring.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}\left(x+2\right)-6$$

\frac{8}{3} ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{8}{3}\times 2-6$$

\frac{8}{3}\times 2 ni yagona kasrga aylantiring.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{8\times 2}{3}-6$$

16 hosil qilish uchun 8 va 2 ni ko'paytirish.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{16}{3}-6$$

6 ni \frac{18}{3} kasrga o‘giring.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{16}{3}-\frac{18}{3}$$

\frac{16}{3} va \frac{18}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{16-18}{3}$$

-2 olish uchun 16 dan 18 ni ayirish.

$$48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x-\frac{2}{3}$$

\frac{3}{8}x-\frac{1}{8} natijani olish uchun 3x-1 ning har bir ifodasini 8 ga bo‘ling.

$$48x-24\left(2x-\left(\frac{3}{8}x-\frac{1}{8}\right)\right)=\frac{8}{3}x-\frac{2}{3}$$

\frac{3}{8}x-\frac{1}{8} teskarisini topish uchun har birining teskarisini toping.

$$48x-24\left(2x-\frac{3}{8}x-\left(-\frac{1}{8}\right)\right)=\frac{8}{3}x-\frac{2}{3}$$

-\frac{1}{8} ning teskarisi \frac{1}{8} ga teng.

$$48x-24\left(2x-\frac{3}{8}x+\frac{1}{8}\right)=\frac{8}{3}x-\frac{2}{3}$$

\frac{13}{8}x ni olish uchun 2x va -\frac{3}{8}x ni birlashtirish.

$$48x-24\left(\frac{13}{8}x+\frac{1}{8}\right)=\frac{8}{3}x-\frac{2}{3}$$

-24 ga \frac{13}{8}x+\frac{1}{8} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$48x-24\times \frac{13}{8}x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}$$

-24\times \frac{13}{8} ni yagona kasrga aylantiring.

$$48x+\frac{-24\times 13}{8}x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}$$

-312 hosil qilish uchun -24 va 13 ni ko'paytirish.

$$48x+\frac{-312}{8}x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}$$

-39 ni olish uchun -312 ni 8 ga bo‘ling.

$$48x-39x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}$$

\frac{-24}{8} hosil qilish uchun -24 va \frac{1}{8} ni ko'paytirish.

$$48x-39x+\frac{-24}{8}=\frac{8}{3}x-\frac{2}{3}$$

-3 ni olish uchun -24 ni 8 ga bo‘ling.

$$48x-39x-3=\frac{8}{3}x-\frac{2}{3}$$

9x ni olish uchun 48x va -39x ni birlashtirish.

$$9x-3=\frac{8}{3}x-\frac{2}{3}$$

Ikkala tarafdan \frac{8}{3}x ni ayirish.

$$9x-3-\frac{8}{3}x=-\frac{2}{3}$$

\frac{19}{3}x ni olish uchun 9x va -\frac{8}{3}x ni birlashtirish.

$$\frac{19}{3}x-3=-\frac{2}{3}$$

3 ni ikki tarafga qo’shing.

$$\frac{19}{3}x=-\frac{2}{3}+3$$

3 ni \frac{9}{3} kasrga o‘giring.

$$\frac{19}{3}x=-\frac{2}{3}+\frac{9}{3}$$

-\frac{2}{3} va \frac{9}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{19}{3}x=\frac{-2+9}{3}$$

7 olish uchun -2 va 9'ni qo'shing.

$$\frac{19}{3}x=\frac{7}{3}$$

Ikki tarafini \frac{3}{19} va teskari kasri \frac{19}{3} ga ko‘paytiring.

$$x=\frac{7}{3}\times \frac{3}{19}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{7}{3} ni \frac{3}{19} ga ko‘paytiring.

$$x=\frac{7\times 3}{3\times 19}$$

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$x=\frac{7}{19}$$