// Numbas version: exam_results_page_options {"name": "Solving linear equations: one step: multiplying or dividing ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "g", "f", "ans3", "h", "j", "ans4"], "name": "Solving linear equations: one step: multiplying or dividing ", "tags": ["algebra", "balancing equations", "Linear equations", "linear equations", "one step equations", "rearranging equations", "solving equations", "Solving equations"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "

Given $\\var{a}x=\\var{b}$, we can rearrange the equation to that find $x=$ [[0]].

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Given $\\var{a}x=\\var{b}$, we divide both sides by $\\var{a}$ to get $x$ by itself.

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$\\var{a}x$$=$$\\var{b}$
 
$\\displaystyle{\\frac{\\var{a}x}{\\var{a}}}$$=$$\\displaystyle{\\frac{\\var{b}}{\\var{a}}}$
 
$x$$=$$\\displaystyle{\\simplify{{b}/{a}}}$
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Given $\\var{c}y=\\var{d}$,  $y=$ [[0]].

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Given $\\var{c}y=\\var{d}$, we divide both sides by $\\var{c}$ to get $y$ by itself.

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$\\var{c}y$$=$$\\var{d}$
 
$\\displaystyle{\\frac{\\var{c}y}{\\var{c}}}$$=$$\\displaystyle{\\frac{\\var{d}}{\\var{c}}}$
 
$y$$=$$\\displaystyle{\\simplify{{d}/{c}}}$
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Rearrange $\\displaystyle{\\frac{z}{\\var{f}}}=\\var{g}$ to determine the value of $z$.

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$z=$ [[0]]

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Given $\\displaystyle{\\frac{z}{\\var{f}}}=\\var{g}$, we multiply both sides by $\\var{f}$ to get $z$ by itself.

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$\\displaystyle{\\frac{z}{\\var{f}}}$$=$$\\var{g}$
 
$\\displaystyle{\\frac{z}{\\var{f}}}\\times \\var{f}$$=$$\\var{g}\\times\\var{f}$
 
$z$$=$$\\var{ans3}$
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Solve $\\displaystyle{\\var{h}=-\\frac{a}{\\var{j}}}$ for $a$.

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$a=$ [[0]]

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Given $\\displaystyle{\\var{h}=-\\frac{a}{\\var{j}}}$, we multiply both sides by $-\\var{j}$ to get $a$ by itself.

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$\\var{h}$$=$$\\displaystyle{-\\frac{a}{\\var{j}}}$
 
$\\var{h}\\times(-\\var{j})$$=$$\\displaystyle{-\\frac{a}{\\var{j}}\\times(-\\var{j})}$
 
$\\var{ans4}$$=$$a$
 
$a$$=$$\\var{ans4}$
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