Skillnad mellan versioner av "1.6a Lösning 12b"
Från Mathonline
Taifun (Diskussion | bidrag) m |
Taifun (Diskussion | bidrag) m |
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| Rad 14: | Rad 14: | ||
:<math> \underline{x \; > \; 0 {\rm :}} \quad\;\, 1 \;\; < \;\;\; x \;\;\; < \;\;\; 5 </math> | :<math> \underline{x \; > \; 0 {\rm :}} \quad\;\, 1 \;\; < \;\;\; x \;\;\; < \;\;\; 5 </math> | ||
| − | :<math> \begin{array}{lrcccl} \underline{x \; < \; 0 {\rm :}} & | + | :<math> \begin{array}{lrcccl} \underline{x \; < \; 0 {\rm :}} & 1 & < & -x & < & 5 \qquad | \;\; \cdot (-1) \end{array}</math> |
Versionen från 6 september 2014 kl. 13.41
- \[\begin{array}{rcl} \left|\,{5 \over x} + x\,\right| & < & 6 \\ \left|\,{5 + x^2 \over x} \,\right| & < & 6 \\ {|5 + x^2| \over |x|} & < & 6 & | \;\; \cdot |x| \\ |5 + x^2| & < & 6\,|x| \qquad & : \; {\rm VL } \; |5 + x^2| > 0 \\ 5 + x^2 & < & 6\,|x| & | \;\; - 6\,|x| \\ x^2 - 6\,|x| + 5 & < & 0 & | \;\; + 4 \\ x^2 - 6\,|x| + 9 & < & 4 & \\ (\,|x|\,-\,3\,)^2 & < & 4 & | \;\; \sqrt{{\color{White} x}} \\ |\,|x|\,-\,3\,| & < & 2 & | \;\; \sqrt{{\color{White} x}} > 0 \\ -2 \;\; < \;\; |x|\,-\,3\, & < & 2 & | \;\; + 3 \\ 1 \;\; < \;\; |x| & < & 5 \\ \end{array}\]
\[ \underline{x \; > \; 0 {\rm :}} \quad\;\, 1 \;\; < \;\;\; x \;\;\; < \;\;\; 5 \]
\[ \begin{array}{lrcccl} \underline{x \; < \; 0 {\rm :}} & 1 & < & -x & < & 5 \qquad | \;\; \cdot (-1) \end{array}\]
