4x-1/5+x+2/2x-7=8x-3/10-13/10 eching

$$\frac { 4 x - 1 } { 5 } + \frac { x + 2 } { 2 x - 7 } = \frac { 8 x - 3 } { 10 } - \frac { 13 } { 10 }$$

x uchun yechish

$$x = \frac{39}{19} = 2\frac{1}{19} \approx 2,052631579$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati \frac{7}{2} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 10\left(2x-7\right) ga, 5,2x-7,10 ning eng kichik karralisiga ko‘paytiring.

$$\left(4x-14\right)\left(4x-1\right)+10\left(x+2\right)=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

4x-14 ga 4x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$16x^{2}-60x+14+10\left(x+2\right)=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

10 ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16x^{2}-60x+14+10x+20=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

-50x ni olish uchun -60x va 10x ni birlashtirish.

$$16x^{2}-50x+14+20=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

34 olish uchun 14 va 20'ni qo'shing.

$$16x^{2}-50x+34=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

2x-7 ga 8x-3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$16x^{2}-50x+34=16x^{2}-62x+21+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

-13 hosil qilish uchun 10 va -\frac{13}{10} ni ko'paytirish.

$$16x^{2}-50x+34=16x^{2}-62x+21-13\left(2x-7\right)$$

-13 ga 2x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$16x^{2}-50x+34=16x^{2}-62x+21-26x+91$$

-88x ni olish uchun -62x va -26x ni birlashtirish.

$$16x^{2}-50x+34=16x^{2}-88x+21+91$$

112 olish uchun 21 va 91'ni qo'shing.

$$16x^{2}-50x+34=16x^{2}-88x+112$$

Ikkala tarafdan 16x^{2} ni ayirish.

$$16x^{2}-50x+34-16x^{2}=-88x+112$$

0 ni olish uchun 16x^{2} va -16x^{2} ni birlashtirish.

$$-50x+34=-88x+112$$

88x ni ikki tarafga qo’shing.

$$-50x+34+88x=112$$

38x ni olish uchun -50x va 88x ni birlashtirish.

$$38x+34=112$$

Ikkala tarafdan 34 ni ayirish.

$$38x=112-34$$

78 olish uchun 112 dan 34 ni ayirish.

$$38x=78$$

Ikki tarafini 38 ga bo‘ling.

$$x=\frac{78}{38}$$

\frac{78}{38} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{39}{19}$$