:)

[fanny elise]

Løs likningene og ulikheten:
a) x^2 -4x = 0
b)1/2 (x-2/3) + 3 <2x
c)2/3 x +4 = 3 - (x-1)/2

d) lg x = 3
e) 4lg (x-1) - 8 = 0
f) Løs likningssettet ved regning: 2x + 3y = 12
3x - 6y = -3

[ettam]

a)

[tex]x^2 -4x = 0 [/tex]

[tex]x(x-4) = 0[/tex]

[tex]\underline{\underline{x = 0}} \ \ [/tex] eller [tex]\ \ \underline{\underline{x= 4}}[/tex]

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b)

[tex]\frac12 (x - \frac23) + 3 < 2x \ \ | \ \cdot 2[/tex]

[tex]x - \frac23 + 6 < 4x \ \ | \ \cdot 3[/tex]

[tex]3x - 2 +18 < 12x[/tex]

[tex]3x-12x < 2 -18[/tex]

[tex]-9x < -16[/tex]

[tex]\underline{\underline{x > \frac{16}{9}}}[/tex]



Resten tar jeg senere, eller noen andre kan prøve...

[ettam]

c)

[tex]\frac23 x + 4 = 3 - \frac{x-1}{2} \ \ | \cdot 6[/tex]

[tex]4x + 24 = 18 - (x-1)3[/tex]

[tex]4x + 24 = 18 - 3x + 3[/tex]

[tex]4x + 3x = 18 + 3 - 24[/tex]

[tex]7x = -3[/tex]

[tex]\underline{\underline{x = - \frac37}}[/tex]

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d)

[tex]lg x = 3 [/tex]

[tex]10^{lg x}= 10^3[/tex]

[tex]\underline{\underline{x = 1000}}[/tex]

_____________________________________________________________________________


e)

[tex]4lg (x-1) - 8 = 0[/tex]

[tex]4lg(x-1) = 8[/tex]

[tex]lg(x-1) = 2[/tex]

[tex]10^{lg(x-1) = 10^2}[/tex]

[tex]x - 1 = 100[/tex]

[tex]\underline{\underline{x = 101}}[/tex]

[ettam]

f)

1) [tex]2x + 3y = 12 \ \ | \cdot (-3) [/tex]

2) [tex]3x - 6y = -3\ \ | \cdot 2[/tex]


1) [tex]-6x - 9y = -36[/tex]

2) [tex]6x - 12y = -6[/tex]
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[tex]-21y = -42[/tex]

[tex]y = 2[/tex]

Setter [tex]\ y = 2 \[/tex] inn i 1), og får:

[tex]2x + 3\cdot2 = 12[/tex]

[tex]2x + 6 = 12[/tex]

[tex]2x = 6[/tex]

[tex]x = 3[/tex]

Løsning: [tex]\underline{\underline{x = 3}} \ [/tex] og [tex] \ \underline{\underline{y = 2}}[/tex]