5.
[tex](2 \sqrt{2} - 1 {)}^{2} + (2 \sqrt{2} + 1 {)}^{2} = {x}^{2} \\ 8 - 4 \sqrt{2} + 1 + 8 + 4 \sqrt{2} + 1 = {x}^{2} \\ 9- 4 \sqrt{2} + 9 + 4 \sqrt{2} = {x}^{2} \\ {x}^{2} = 18 \\ x = \sqrt{18} \\ x = \sqrt{9 \times 2} \\ \boxed{x = 3 \sqrt{2} }[/tex]
6.
[tex]2x - \frac{x + 1}{3} \leqslant 4 - 5x | \times 3 \\ 6x - (x + 1) \leqslant 12 - 15x \\ 6x - x - 1 \leqslant 12 - 15x \\ 5x - 1 \leqslant 12 - 15x | \bold{+ 15x }\\ 20x - 1\leqslant 12 | \bold{ + 1} \\ 20x \leqslant 13 | \bold{\div 20} \\ \boxed{ x \leqslant \frac{13}{20} }[/tex]
