1/2[1+1/4(3z-1)]=2z/3-1/2 eching

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

z uchun yechish

$$z=3$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 12 ga, 2,4,3 ning eng kichik karralisiga ko‘paytiring.

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

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

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

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

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

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

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

1 ni \frac{4}{4} kasrga o‘giring.

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

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

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

3 olish uchun 4 dan 1 ni ayirish.

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

6 ga \frac{3}{4}+\frac{3}{4}z ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

6\times \frac{3}{4} ni yagona kasrga aylantiring.

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

18 hosil qilish uchun 6 va 3 ni ko'paytirish.

$$\frac{18}{4}+6\times \frac{3}{4}z=4\times 2z-6$$

\frac{18}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{9}{2}+6\times \frac{3}{4}z=4\times 2z-6$$

6\times \frac{3}{4} ni yagona kasrga aylantiring.

$$\frac{9}{2}+\frac{6\times 3}{4}z=4\times 2z-6$$

18 hosil qilish uchun 6 va 3 ni ko'paytirish.

$$\frac{9}{2}+\frac{18}{4}z=4\times 2z-6$$

\frac{18}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{9}{2}+\frac{9}{2}z=4\times 2z-6$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$\frac{9}{2}+\frac{9}{2}z=8z-6$$

Ikkala tarafdan 8z ni ayirish.

$$\frac{9}{2}+\frac{9}{2}z-8z=-6$$

-\frac{7}{2}z ni olish uchun \frac{9}{2}z va -8z ni birlashtirish.

$$\frac{9}{2}-\frac{7}{2}z=-6$$

Ikkala tarafdan \frac{9}{2} ni ayirish.

$$-\frac{7}{2}z=-6-\frac{9}{2}$$

-6 ni -\frac{12}{2} kasrga o‘giring.

$$-\frac{7}{2}z=-\frac{12}{2}-\frac{9}{2}$$

-\frac{12}{2} va \frac{9}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$-\frac{7}{2}z=\frac{-12-9}{2}$$

-21 olish uchun -12 dan 9 ni ayirish.

$$-\frac{7}{2}z=-\frac{21}{2}$$

Ikki tarafini -\frac{2}{7} va teskari kasri -\frac{7}{2} ga ko‘paytiring.

$$z=-\frac{21}{2}\left(-\frac{2}{7}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{21}{2} ni -\frac{2}{7} ga ko‘paytiring.

$$z=\frac{-21\left(-2\right)}{2\times 7}$$

\frac{-21\left(-2\right)}{2\times 7} kasridagi ko‘paytirishlarni bajaring.

$$z=\frac{42}{14}$$

3 ni olish uchun 42 ni 14 ga bo‘ling.

$$z=3$$