Question

Найдите решение уравнения:
1) 7 |х| - 5 |х| = 13;
2) 1,1 |х| + 4,9 |х| = 27;
3) 2/3 |х| - 8,5 + 1/7 |х| = 0;
4) 5/12 |х| - 3,8 + 1/9 |х| = 0.
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Answer 1

1) $x=6.5 или x = -6.5$

2) $x=4.5 \\x=-4.5$

3) $x=10.5\\x=-10.5$

4) $x=7.2\\x=-7.2$

Пошаговое объяснение:

$7|x|-5|x| =13\\2|x| = 13\\|x| = 6.5\\x=6.5 или x = -6.5$

$1.1|x|+4.9|x| = 27\\6|x| = 27\\|x| = 4.5\\x=4.5 \\x=-4.5$

$\frac{2}{3} |x| -8.5 +\frac{1}{7} |x| = 0\\\frac{14}{21}|x|+\frac{3}{21}|x| = 8.5\\\frac{17}{21}|x| = \frac{85}{10}\\ |x| = \frac{85\cdot 21}{10 \cdot 17} = \frac{5 \cdot 21}{10} = 10.5\\ x=10.5\\x=-10.5$

$\frac{5}{12} |x| - 3.8+ \frac{1}{9}|x| = 0 \\\frac{5}{12} |x|+ \frac{1}{9}|x| = 3.8\\\frac{15}{36} |x|+ \frac{4}{36}|x| = 3.8\\\\\frac{19}{36} |x|= 3.8\\|x|=7.2\\x=7.2\\x=-7.2$