373 Вправа 373Алгебра 8 клас Бевз 2025 · § 8 · стор. 77

373. Розв’яжи рівняння.

а) ${\displaystyle \frac{4+x}{3x}=}$${\displaystyle \frac{1}{2}}$;

допустимі ${\displaystyle x\ne 0}$;

${\displaystyle 2(4+x)=}$${\displaystyle 3x}$;

${\displaystyle 8+2x=}$${\displaystyle 3x}$;

${\displaystyle 2x-3x=}$${\displaystyle -8}$;

${\displaystyle -x=}$${\displaystyle -8}$;

${\displaystyle x=}$${\displaystyle 8}$;

б) ${\displaystyle \frac{7-2x}{x+1}=}$${\displaystyle \frac{2}{3}}$;

допустимі ${\displaystyle x\ne -1}$;

${\displaystyle 3(7-2x)=}$${\displaystyle 2(x+1)}$;

${\displaystyle 21-6x=}$${\displaystyle 2x+2}$;

${\displaystyle -6x-2x=}$${\displaystyle 2-21}$;

${\displaystyle -8x=}$${\displaystyle -19}$;

${\displaystyle x=}$${\displaystyle \frac{-19}{-8}}$;

${\displaystyle x=}$${\displaystyle \frac{19}{8}=}$${\displaystyle 2\frac{3}{8}}$;

в) ${\displaystyle \frac{x+5}{x-3}=}$${\displaystyle \frac{3}{4}}$;

допустимі ${\displaystyle x\ne 3}$;

${\displaystyle 4(x+5)=}$${\displaystyle 3(x-3)}$;

${\displaystyle 4x+20=}$${\displaystyle 3x-9}$;

${\displaystyle 4x-3x=}$${\displaystyle -9-20}$;

${\displaystyle x=}$${\displaystyle -29}$;

г) ${\displaystyle \frac{3x^2-4}{2x}=}$${\displaystyle x}$;

допустимі ${\displaystyle x\ne 0}$;

${\displaystyle 3x^2-4=}$${\displaystyle 2x\cdot x}$;

${\displaystyle 3x^2-4=}$${\displaystyle 2x^2}$;

${\displaystyle 3x^2-2x^2=}$${\displaystyle 4}$;

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

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

ґ) ${\displaystyle \frac{3x^2+5}{x^2-1}=}$${\displaystyle 4}$;

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

${\displaystyle 3x^2+5=}$${\displaystyle 4(x^2-1)}$;

${\displaystyle 3x^2+5=}$${\displaystyle 4x^2-4}$;

${\displaystyle 3x^2-4x^2=}$${\displaystyle -4-5}$;

${\displaystyle -x^2=}$${\displaystyle -9}$;

${\displaystyle x^2=}$${\displaystyle 9}$;

${\displaystyle x=}$${\displaystyle \pm 3}$;

д) ${\displaystyle \frac{9-4x^2}{3x}=}$${\displaystyle -x}$;

допустимі ${\displaystyle x\ne 0}$;

${\displaystyle 9-4x^2=}$${\displaystyle -x\cdot 3x}$;

${\displaystyle 9-4x^2=}$${\displaystyle -3x^2}$;

${\displaystyle -4x^2+3x^2=}$${\displaystyle -9}$;

${\displaystyle -x^2=}$${\displaystyle -9}$;

${\displaystyle x^2=}$${\displaystyle 9}$;

${\displaystyle x=}$${\displaystyle \pm 3}$.