# Oppgaver: Lineære ulikheter


:::::::::::::::{exercise} Oppgave 1
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Figuren nedenfor viser grafen til $f(x) = x + 3$.

Bruk figuren til å løse ulikheten 

$$
x + 3 < 0.
$$

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:::::::::::::{tab-item} b
Figuren nedenfor viser grafen til $f(x) = -2x + 4$. 

Bruk figuren til å løse ulikheten

$$
-2x + 4 \leq 0.
$$


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:::::::::::::{tab-item} c
Figuren nedenfor  viser grafen til $f(x) = \dfrac{1}{2}x - 1$. 

Bruk figuren til å løse ulikheten

$$
\frac{1}{2}x - 1 > 0.
$$

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:::::::::::::{tab-item} d
Figuren nedenfor viser grafen til $f(x) = 3x - 6$. 

Bruk figuren til å løse ulikheten

$$
3x - 6 \geq 0.
$$

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:::::::::::::::{exercise} Oppgave 2
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Bruk graftegner i Geogebra til å løse ulikhetene nedenfor.


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$$
2x + 6 \leq -x + 3
$$
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$$
-2x + 3 > 1
$$
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$$
\dfrac{3}{2}x + 1 < x + 2
$$
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:::::::::::::{tab-item} d

$$
2x + 5 \geq -3x + 2
$$


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:::::::::::::::{exercise} Oppgave 3
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Løs ulikhetene algebraisk. 

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$$
2x + 5 < -2
$$
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$$
3x + 2 > -2x + 7
$$
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:::::::::::::{tab-item} c
$$
\dfrac{1}{5}x + 3 \leq -2x + 3
$$


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:::::::::::::{tab-item} d
$$
-2x + \dfrac{1}{2} \geq 5x + 3
$$


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:::::::::::::::{exercise} Oppgave 4
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::::{hints} Hvordan løser jeg en ulikhet med CAS?
Nedenfor ser du en gif som løser ulikheten

$$
2x + 3 < -3x + 5
$$

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Fra utskriften ser vi at løsningen er

$$
x < \dfrac{2}{5}
$$

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Bruk CAS til å løse ulikhetene.

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$$
-2x + 3 > 2x + 6
$$


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$$
3x - 2 \geq \dfrac{1}{3}x + 1
$$


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:::::::::::::{tab-item} c

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$$
-2x + 9 \leq 3x + 5
$$


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:::::::::::::{tab-item} d

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$$
-7x + 3 < 3x + 7
$$


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:::::::::::::::{exercise} Oppgave 5
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I figuren nedenfor vises grafene til to lineære funksjoner $f$ og $g$.

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Løs ulikheten 

$$
f(x) < 0
$$
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:::::::::::::{tab-item} b
Løs ulikheten

$$
g(x) \geq 3
$$

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:::::::::::::{tab-item} c
Løs ulikheten 

$$
f(x) \leq g(x)
$$


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:::::::::::::::{exercise} Oppgave 6
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To lineære funksjoner $f$ og $g$ er gitt ved

$$
f(x) = -\dfrac{1}{2}x + 3 \qog g(x) = 2(x - 1) + 3
$$


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Løs ulikheten

$$
f(x) > 0
$$

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Løs ulikheten


$$
g(x) < -2
$$

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:::::::::::::{tab-item} c



Løs ulikheten

$$
f(x) \geq g(x)
$$

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