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Including brackets and fractions.</p>", "licence": "None specified"}, "statement": "<p>Solve the following equations to find $x$:</p>", "advice": "<h3><strong>part a)</strong></h3>\n<p>\\[\\simplify{{a}x+{b} = {c}} \\]</p>\n<p>The first step is to isolate all the $x$-terms to one side of the equation.</p>\n<p>To do that we will {add} $\\var{abs(b)}$ onto both sides:</p>\n<p>\\[\\var{a}x &nbsp;= \\simplify{{c-b}} \\]</p>\n<p>Now we need to divide both sides by the coefficient of $x$, to leave just one $x$.</p>\n<p>Dividing both sides by $\\var{a}$,</p>\n<p>\\[ &nbsp;x = {\\simplify{({c}-{b})/{a}}} \\]</p>\n<p></p>\n<h3><strong>part b)</strong></h3>\n<p>&nbsp;\\[ \\frac{\\simplify{{d}x + {f}}}{\\var{g}} = \\var{h} \\]<br/><br/>The first step is to rearrange by removing the fraction on the left. &nbsp;To do this we mulitply both sides by $\\var{g}$.<br/><br/>\\[ \\begin{split} \\frac{\\simplify{{d}x + {f}}}{\\var{g}} \\times \\var{g}&nbsp; &amp;= \\var{h} \\times \\var{g} \\\\\\\\ \\simplify{{d}x + {f}} &amp;= \\var{h*g} \\end{split} \\]<br/><br/>Next we&nbsp;isolate all the $x$-terms onto one side of the equation.<br/><br/>To do that we will {add2} $\\var{abs(f)}$ on both sides:<br/><br/>\\[ \\begin{split}&nbsp;\\var{d}x &amp;= \\simplify[]{{h*g}-{f}} \\\\ &amp;= \\simplify[]{{h*g-f}} \\end{split}\\]<br/><br/>Finally we need to divide both sides by the coefficient of $x$, to leave just one $x$.</p>\n<p>Dividing both sides by $\\var{d}$,<br/><br/>\\[x = \\simplify[fractionNumbers]{{(h*g-f)/d}} &nbsp;\\]</p>\n<p></p>\n<h3>part c)</h3>\n<p>\\[ \\simplify{{b}({c}x+{g})} = \\var{d} \\]</p>\n<p>Even though this looks different, this is quite similar to part b). &nbsp;We just have a multiplication rather than a division to deal with as the first step.<br/><br/>Rearrange to remove the multiplication on the left. &nbsp;To do this we divide both sides by $\\var{b}$:<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/>Next we&nbsp;isolate all the $x$-terms onto one side of the equation.<br/><br/>To do that we will {add3} $\\var{abs(g)}$ on both sides:<br/><br/>\\[ \\begin {split} \\simplify{{c}x + {g}} &nbsp;&nbsp;\\var{add3sym} &nbsp; \\var{abs(g)} &amp;= \\simplify[fractionNumbers]{{d/b}}&nbsp;\\var{add3sym} \\var{abs(g)} \\\\ \\var{c}x &amp;= \\simplify[fractionNumbers]{{d/b-g}} \\end{split} \\]<br/><br/>Finally we need to divide both sides by the coefficient of $x$, to leave just one $x$</p>\n<p>Dividing both sides by $\\var{c}$:<br/><br/>\\[ x = &nbsp;\\simplify[fractionNumbers]{{(d/b-g)/c}} \\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-20..20 except 0 except 1 except -1)", "description": "", "templateType": "anything", 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