Question

Verify that | x + y | ≤ | x | + | y | by taking x = 2/3, y = - 3/5 .

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Answer 1

$= = > \: \: |x + y| \leqslant |x| + |y|$

==> x = 2/3 , y = -3/5

$= = > \: \: | \frac{2}{3} - \frac{3}{5} | \leqslant | \frac{2}{3} | + | - \frac{3}{5} | \\ \\ = = > \: \: | \frac{10 - 9}{15} | \leqslant \frac{2}{3} + \frac{3}{5} \\ \\ = = > \: \: \frac{1}{15} \leqslant \frac{10 + 9}{15} \\ \\ = = > \: \: \frac{1}{ \cancel{15}} \leqslant \frac{19}{ \cancel{15}} \\ \\ = = > \: \: 1 \leqslant 19$

Hence, Proved.