4x-7/12x+3=x-16/3x+5 eching

$$\frac { 4 x - 7 } { 12 x + 3 } = \frac { x - 16 } { 3 x + 5 }$$

x uchun yechish

$$x=-\frac{13}{188}\approx -0,069148936$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x qiymati -\frac{5}{3},-\frac{1}{4} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 3\left(3x+5\right)\left(4x+1\right) ga, 12x+3,3x+5 ning eng kichik karralisiga ko‘paytiring.

$$\left(3x+5\right)\left(4x-7\right)=\left(12x+3\right)\left(x-16\right)$$

3x+5 ga 4x-7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$12x^{2}-x-35=\left(12x+3\right)\left(x-16\right)$$

12x+3 ga x-16 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$12x^{2}-x-35=12x^{2}-189x-48$$

Ikkala tarafdan 12x^{2} ni ayirish.

$$12x^{2}-x-35-12x^{2}=-189x-48$$

0 ni olish uchun 12x^{2} va -12x^{2} ni birlashtirish.

$$-x-35=-189x-48$$

189x ni ikki tarafga qo’shing.

$$-x-35+189x=-48$$

188x ni olish uchun -x va 189x ni birlashtirish.

$$188x-35=-48$$

35 ni ikki tarafga qo’shing.

$$188x=-48+35$$

-13 olish uchun -48 va 35'ni qo'shing.

$$188x=-13$$

Ikki tarafini 188 ga bo‘ling.

$$x=\frac{-13}{188}$$

\frac{-13}{188} kasri manfiy belgini olib tashlash bilan -\frac{13}{188} sifatida qayta yozilishi mumkin.

$$x=-\frac{13}{188}$$