26 lines
793 B
TeX
26 lines
793 B
TeX
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\begin{deloppgaver}
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\delo
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\begin{align*}
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|5-2x| &< 3 \\
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-3 < 5-2x &< 3 \\
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-3 < 5-2x \quad &\vee \quad 5-2x < 3 \\
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-8 < 2x \quad &\vee \quad -2x < -2 \\
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8 > 2x \quad &\vee \quad 2x > 2 \\
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4 > x \quad &\vee \quad x > 1 \\
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x &\in \left(1,4\right)
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\end{align*}
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\delo
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\begin{align*}
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|x^2 - 3| &< 6 \\
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-6 < x^2-3 \quad &\vee \quad x^2-3 < 6 \\
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-3 < x^2 \quad &\vee \quad x*2 < 9 \\
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\pm\sqrt{-3} < x \quad &\vee \quad x < \pm 3 \\
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\end{align*}
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Ettersom $\sqrt{-3}$ er et imaginert tall, er dette ikke et valid skjæringspunkt. Vi tar den ikke med i beregningen.
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\[ x \in (-3,3) \]
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\end{deloppgaver}
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