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Solve linear equations with unkowns on both sides. Including brackets and fractions.

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Løs likningene. Oppgi svaret som et helt tall eller en brøk.

", "advice": "

Oppgave a)

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I $\\simplify{{l}({m}w-{n}) = {p}w+{q}}$, må vi først løse opp parentesene, deretter samler vi alle $w$'ene på venstre side og alle tallene på høyre side. Til slutt deler vi på tallet foran $w$ (koeffisienten til $w$) for å få $w$ alene.

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\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\simplify{{l}({m}w-{n})}$$=$$\\simplify{{p}w+{q}}$ 
 
$\\simplify{{l*m}w-{n*l}}$$=$$\\simplify{{p}w+{q}}$
 
$\\simplify[!cancelTerms,unitFactor]{{l*m}w-{n*l}-{p}w}$$=$$\\simplify[!cancelTerms,unitFactor]{{p}w+{q}-{p}w}$(trekker fra $\\var{p}w$ på begge sider)
 
$\\simplify{{l*m-p}w-{n*l}}$$=$$\\var{q}$
 
$\\var{l*m-p}w-\\var{n*l}+\\var{n*l}$$=$$\\var{q}+\\var{n*l}$(legger til $\\var{n*l}$ på begge sider)
 
$\\var{l*m-p}w$$=$$\\var{q+n*l}$
 
$\\displaystyle{\\frac{\\var{l*m-p}w}{\\var{l*m-p}}}$$=$$\\displaystyle{\\frac{\\var{q+n*l}}{\\var{l*m-p}}}$(deler på $\\var{l*m-p}$ på begge sider)
 
$w$$=$$\\displaystyle{\\simplify{{q+n*l}/{l*m-p}}} $
\n

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Oppgave b)

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I uttrykket $\\displaystyle{\\frac{\\var{d}y}{y-\\var{f}}}=\\var{g}$ må vi multiplisere med $(y-\\var{f})$ for å bli kvitt brøken, deretter får vi alle $y$'ene på ene siden og tallene på andre siden, og til slutt deler vi på koeffisienten til $y$ for å få $y$ alene..

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\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\displaystyle{\\frac{\\var{d}y}{y-\\var{f}}}$$=$$\\var{g}$ 
 
$\\displaystyle{\\frac{\\var{d}y}{y-\\var{f}}}\\cdot(y-\\var{f})$$=$$\\var{g}\\cdot (y-\\var{f})$(multipliserer med (y-\\var{f}) )
 
$\\var{d}y$$=$$\\simplify[unitFactor]{{g}y+{-g*f}}$
 
$\\simplify[!cancelTerms,unitFactor]{{d}y+{-g}y}$ $=$$\\simplify[!cancelTerms,unitFactor]{{-g*f}}$(legger til $\\simplify{{-g}y}$ på begge sider
 
$\\var{d-g}y$$=$$\\var{-g*f}$
 
$\\displaystyle{\\frac{\\var{d-g}y}{\\var{d-g}}}$$=$$\\displaystyle{\\frac{\\var{-g*f}}{\\var{d-g}}}$(deler på $\\var{d-g}$ på begge sider)
 
 $y$$=$$\\displaystyle{\\simplify{{-g*f}/{d-g}}}$
\n

Oppgave c)

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I uttrykket $\\displaystyle{\\frac{x+\\var{add}}{\\var{denom1}}+\\frac{x}{\\var{denom2}}=\\var{right}}$ må vi multiplisere begge sider med $\\var{denom1}$ og by $\\var{denom2}$ for å bli kvitt alle brøkene, deretter får vi alle $x$'ene på ene siden og tallene på andre siden,og til slutt deler vi begge sidene på koeffisienten til $x$ for å få $x$ alene.

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\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\displaystyle{\\frac{x+\\var{add}}{\\var{denom1}}+\\frac{x}{\\var{denom2}}}$$=$$\\var{right}$ 
 
$\\displaystyle{\\left(\\frac{x+\\var{add}}{\\var{denom1}}\\right)\\cdot\\var{denom1}+\\left(\\frac{x}{\\var{denom2}}\\right)\\cdot\\var{denom1}}$$=$$\\var{right}\\cdot \\var{denom1}$(multipliserer alle ledd med $\\var{denom1}$)
 
$\\displaystyle{x+\\var{add}+\\frac{\\var{denom1}x}{\\var{denom2}}}$$=$$\\var{r1}$
 
$\\displaystyle{(x+\\var{add})\\cdot\\var{denom2}+\\left(\\frac{\\var{denom1}x}{\\var{denom2}}\\right)\\cdot\\var{denom2}}$ $=$$\\var{r1}\\cdot\\var{denom2}$(multipliserer alle ledd med $\\var{denom2}$)
 
$\\displaystyle{\\var{denom2}x+\\var{a2}+\\var{denom1}x}$$=$$\\var{r12}$
 
$\\var{sumdeno}x+\\var{a2}$$=$$\\var{r12}$(samler ledd av samme type)
 
 $\\var{sumdeno}x$$=$$\\var{r12}-\\var{a2}$(samler ledd av samme type)
 
$\\var{sumdeno}x$$=$$\\var{top}$
 
$x$$=$$\\displaystyle{\\simplify{{top}/({sumdeno})}} $(deler med koeffisienten til $x$)
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Løs  $\\simplify{{l}({m}w-{n}) = {p}w+{q}}$

\n

$w=$ [[0]]

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Gitt $\\displaystyle{\\frac{\\var{d}y}{y-\\var{f}}}=\\var{g}$,  

\n

$y=$ [[0]].

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Løs $\\displaystyle{\\frac{x+\\var{add}}{\\var{denom1}}+\\frac{x}{\\var{denom2}}=\\var{right}}$.

\n

$x=$ [[0]]

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