// Numbas version: finer_feedback_settings
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Oppgi svarene som heltall eller br&oslash;k.</p>", "advice": "<h3><strong>Oppgave a)</strong></h3>\n<p>\\[\\simplify{{a}x+{b} = {c}} \\]</p>\n<p>F&oslash;rst samler vi alle&nbsp; $x$-leddene p&aring; den ene siden av likningen.</p>\n<p>For &aring; f&aring; det til m&aring; vi {add[0]} $\\var{abs(b)}$ {add[1]} begge sider:</p>\n<p>\\[\\simplify[all,!collectNumbers]{{a}x+{b} - {b} = {c} - {b}}&nbsp;\\]</p>\n<p>\\[\\var{a}x &nbsp;= \\simplify{{c-b}} \\]</p>\n<p>For &aring; f&aring; $x$ alene deler vi p&aring; koeffisienten til $x$ (tallet foran $x$) p&aring; begge sider.</p>\n<p>Vi deler p&aring; $\\var{a}$:</p>\n<p>\\[ &nbsp;x = {\\simplify{({c}-{b})/{a}}} \\]</p>\n<p></p>\n<h3><strong>Oppgave b)</strong></h3>\n<p>&nbsp;\\[ \\frac{\\simplify{{d}x + {f}}}{\\var{g}} = \\var{h} \\]<br/><br/>F&oslash;rst vil vi kvitte oss med br&oslash;ken p&aring; venstre side. &nbsp;Det gj&oslash;r vi ved &aring; multiplisere begge sidene med $\\var{g}$:<br/><br/>\\[ \\begin{split} \\frac{\\simplify{{d}x + {f}}}{\\var{g}} \\cdot \\var{g}&nbsp; &amp;= \\var{h} \\cdot \\var{g} \\\\\\\\ \\simplify{{d}x + {f}} &amp;= \\var{h*g} \\end{split} \\]<br/><br/>Det neste vi gj&oslash;r er &aring; samle $x$-leddene p&aring; den ene siden av likningen.<br/><br/>Vi m&aring; da {add2[0]} $\\var{abs(f)}$ {add2[1]} begge sider:<br/><br/>\\[ \\begin{split}&nbsp;\\var{d}x &amp;= \\simplify[]{{h*g}-{f}} \\\\ &amp;= \\simplify[]{{h*g-f}} \\end{split}\\]<br/><br/>Til slutt m&aring; vi dele p&aring; $\\var{d}$ for &aring; f&aring; $x$ alene p&aring; venstre siden.</p>\n<p><br/>\\[x = \\simplify[fractionNumbers]{{(h*g-f)/d}} &nbsp;\\]</p>\n<p></p>\n<h3>Oppgave c)</h3>\n<p>\\[ \\simplify{{b}({c}x+{g})} = \\var{d} \\]</p>\n<p>I oppgave b) var $x$-uttrykket delt p&aring; $\\var{g}$, og vi m&aring;tte da multiplisere for &aring; f&aring; bort nevneren.&nbsp; Her er $x$-uttrykket multiplisert med et tall, og da m&aring; vi dividere for &aring; bli kvitt det-<br/>Vi deler begge sider p&aring; $\\var{b}$:<br/><br/>\\[ \\begin{split} \\frac{\\simplify{{b}({c}x+{g})}}{ \\var{b}} &amp;= \\frac{\\var{d}}{\\var{b}} \\\\ \\\\ \\simplify{{c}x+{g}} &amp;= \\simplify[fractionNumbers]{{d/b}} \\end{split} \\]<br/><br/><br/>Det neste vi gj&oslash;r er &aring; samle $x$-leddene p&aring; den ene siden av likningen.<br/><br/>Vi m&aring; da {add3[0]} $\\var{abs(g)}$ {add3[1]} begge sider:</p>\n<p>\\[ \\begin {split} \\simplify[all,!collectNumbers]{{c}x + {g} - {g}} &amp;= \\simplify[fractionNumbers,!cancelTerms]{{d/b} - {g}}\\\\ \\var{c}x &amp;= \\simplify[fractionNumbers]{{d/b-g}} \\end{split} \\]<br/><br/>Til slutt m&aring; vi dele p&aring; $\\var{c}$for &aring; f&aring; $x$ alene p&aring; venstre siden.<br/>\\[ x = &nbsp;\\simplify[fractionNumbers]{{(d/b-g)/c}} \\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-20..20 except 0 except 1 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