Question

Rozwiąż równanie /załącznik/

Answer 1

Szczegółowe wyjaśnienie:

Z def. wartości bezwzględnej:

|a| = a  dla a ≥ 0

|a| = -a dla a < 0

[tex]|x+8| = 5|x-0,5|\\\\|x+8| = 5|x-\frac{1}{2}|\\\\\\x+8 = 5(x - \frac{1}{2}) \ \ \vee \ \ x+8 = -5(x-\frac{1}{2})\\\\x+8 = 5x-\frac{5}{2} \ \ \ \vee \ \ \ x+8 = -5x+\frac{5}{2}\\\\x-5x = -\frac{5}{2}-8 \ \ \vee \ \ \ x+5x = \frac{5}{2}-8\\\\-4x = -\frac{5}{2}-\frac{16}{2} \ \ \ \vee \ \ \ 6x = \frac{5}{2}-\frac{16}{2}\\\\-4x = -\frac{21}{2} \ \ \ |:(-4) \ \ \ \ \vee \ \ \ \ 6x = -\frac{11}{2} \ \ \ |:6\\\\x = \frac{21}{8} \ \ \ \vee \ \ \ x = -\frac{11}{12}[/tex]

[tex]\underline{x = 2\frac{5}{8} \ \ \ \vee \ \ \ x = -\frac{11}{12}}[/tex]