248° Вправа 248Алгебра 8 клас Тарасенкова 2025 · § 7 · стор. 75

248. Застосуйте основну властивість пропорції та розв’яжіть рівняння:

1) ${\displaystyle \frac{2}{3x}=}$${\displaystyle \frac{8}{21}}$;

ОДЗ: ${\displaystyle x\ne 0}$;

${\displaystyle 8\cdot 3x=}$${\displaystyle 2\cdot 21}$;

${\displaystyle 24x=}$${\displaystyle 42}$ | ${\displaystyle :24}$

${\displaystyle x=}$${\displaystyle \frac{\stackrel{7}{\cancel{42}}}{\underset{4}{\cancel{24}}}}$;

${\displaystyle x=}$${\displaystyle 1,75}$;

2) ${\displaystyle \frac{x-2}{4x}=}$${\displaystyle \frac{5}{8}}$;

ОДЗ: ${\displaystyle x\ne 0}$;

${\displaystyle 8\cdot (x-2)=}$${\displaystyle 5\cdot 4x}$;

${\displaystyle 8x-16=}$${\displaystyle 20x}$;

${\displaystyle 8x-20x=}$${\displaystyle 16}$;

${\displaystyle -12x=}$${\displaystyle 16}$ | ${\displaystyle :\left(-12\right)}$

${\displaystyle x=}$${\displaystyle -\frac{\stackrel{4}{\cancel{16}}}{\underset{3}{\cancel{12}}}}$;

${\displaystyle x=}$${\displaystyle -1\frac{1}{3}}$;

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

ОДЗ: ${\displaystyle 4+x\ne 0}$;

${\displaystyle x\ne -4}$;

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

${\displaystyle 5x=}$${\displaystyle 16+4x}$;

${\displaystyle 5x-4x=}$${\displaystyle 16}$;

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

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

ОДЗ: ${\displaystyle 5-x\ne 0}$;

${\displaystyle x\ne 5}$;

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

${\displaystyle 15x=}$${\displaystyle 15-3x}$;

${\displaystyle 15x+3x=}$${\displaystyle 15}$;

${\displaystyle 18x=}$${\displaystyle 15}$ | ${\displaystyle :18}$

${\displaystyle x=}$${\displaystyle \frac{\stackrel{5}{\cancel{15}}}{\underset{6}{\cancel{18}}}}$;

${\displaystyle x=}$${\displaystyle \frac{5}{6}}$;

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

ОДЗ: ${\displaystyle 1+x\ne 0}$;

${\displaystyle x\ne -1}$;

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

${\displaystyle 4x-8=}$${\displaystyle 3+3x}$;

${\displaystyle 4x-3x=}$${\displaystyle 3+8}$;

${\displaystyle x=}$${\displaystyle 11}$;

6) ${\displaystyle \frac{2-3x}{3-x}=}$${\displaystyle \frac{7}{8}}$;

ОДЗ: ${\displaystyle 3-x\ne 0}$;

${\displaystyle x\ne 3}$;

${\displaystyle 8\cdot (2-3x)=}$${\displaystyle 7\cdot (3-x)}$;

${\displaystyle 16-24x=}$${\displaystyle 21-7x}$;

${\displaystyle -24x+7x=}$${\displaystyle 21-16}$;

${\displaystyle -17x=}$${\displaystyle 5}$ | ${\displaystyle :\left(-17\right)}$

${\displaystyle x=}$${\displaystyle -\frac{5}{17}}$.