375 Вправа 375Алгебра 8 клас Бевз 2025 · § 8 · стор. 77

375. Користуючись властивістю пропорції, розв’яжи рівняння.

а) ${\displaystyle \frac{1}{23-3x}=}$${\displaystyle \frac{1}{2}}$;

допустимі ${\displaystyle x\ne 7\frac{2}{3}}$;

${\displaystyle 23-3x=}$${\displaystyle 2}$;

${\displaystyle -3x=}$${\displaystyle 2-23}$;

${\displaystyle -3x=}$${\displaystyle -21}$;

${\displaystyle x=}$${\displaystyle \frac{-21}{-3}}$;

${\displaystyle x=}$${\displaystyle 7}$;

б) ${\displaystyle \frac{1}{29}=}$${\displaystyle \frac{1}{34y-5}}$;

допустимі ${\displaystyle y\ne \frac{5}{34}}$;

${\displaystyle 34y-5=}$${\displaystyle 29}$;

${\displaystyle 34y=}$${\displaystyle 29+5}$;

${\displaystyle 34y=}$${\displaystyle 34}$;

${\displaystyle y=}$${\displaystyle \frac{34}{34}}$;

${\displaystyle y=}$${\displaystyle 1}$;

в) ${\displaystyle \frac{x}{x+1}=}$${\displaystyle \frac{2}{3}}$;

допустимі ${\displaystyle x\ne -1}$;

${\displaystyle 3x=}$${\displaystyle 2(x+1)}$;

${\displaystyle 3x=}$${\displaystyle 2x+2}$;

${\displaystyle 3x-2x=}$${\displaystyle 2}$;

${\displaystyle x=}$${\displaystyle 2}$;

г) ${\displaystyle \frac{1}{x^2+4}=}$${\displaystyle \frac{1}{4}}$;

${\displaystyle x^2+4=}$${\displaystyle 4}$;

${\displaystyle x^2=}$${\displaystyle 4-4}$;

${\displaystyle x^2=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle 0}$;

ґ) ${\displaystyle \frac{2}{x^2-1}=}$${\displaystyle \frac{1}{12}}$;

допустимі ${\displaystyle x\ne \pm 1}$;

${\displaystyle x^2-1=}$${\displaystyle 2\cdot 12}$;

${\displaystyle x^2-1=}$${\displaystyle 24}$;

${\displaystyle x^2=}$${\displaystyle 24+1}$;

${\displaystyle x^2=}$${\displaystyle 25}$;

${\displaystyle x=}$${\displaystyle \pm 5}$;

д) ${\displaystyle \frac{5x^2-16}{12x}=}$${\displaystyle \frac{x}{3}}$;

допустимі ${\displaystyle x\ne 0}$;

${\displaystyle 3(5x^2-16)=}$${\displaystyle 12x\cdot x}$;

${\displaystyle 15x^2-48=}$${\displaystyle 12x^2}$;

${\displaystyle 15x^2-12x^2=}$${\displaystyle 48}$;

${\displaystyle 3x^2=}$${\displaystyle 48}$;

${\displaystyle x^2=}$${\displaystyle 16}$;

${\displaystyle x=}$${\displaystyle \pm 4}$.