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5d9c4a2 @spicyj Add exercise -- linear inequalities
spicyj authored
1 <!DOCTYPE html>
cde9e9f @jeresig Re-run the exercises through the updated cleaner.
jeresig authored
2 <html data-require="math math-format">
3 <head>
0f0c630 @cbhl Clean up the exercise files using the new cleaning utility. (II)
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4 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
113bddd @spicyj Update the title tags to match real display names
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5 <title>Multi-step linear inequalities</title>
ac1415e @spicyj Use requirejs for module loading
spicyj authored
6 <script data-main="../local-only/main.js" src="../local-only/require.js"></script>
5d9c4a2 @spicyj Add exercise -- linear inequalities
spicyj authored
7 </head>
8 <body>
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9 <div class="exercise">
10 <div class="vars">
11 <var id="A">randRange( 2, 10 )</var>
12 <var id="B">randRangeNonZero( -10, 10 )</var>
0f0c630 @cbhl Clean up the exercise files using the new cleaning utility. (II)
cbhl authored
13 <var id="C" data-ensure="abs( C - A ) &gt; 1">randRange( 2, 10 )</var>
14 <var id="D" data-ensure="D !== B">randRangeNonZero( 2, 10 )</var>
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
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15 <var id="SOLUTION">fractionReduce( D - B, A - C )</var>
5d9c4a2 @spicyj Add exercise -- linear inequalities
spicyj authored
16
62dae32 @cbhl Clean up the exercise files using the new cleaning utility. (IV)
cbhl authored
17 <var id="REL">randFromArray([ "&lt;", "&gt;", "≤", "≥" ])</var>
18 <var id="FREL">{ "&lt;": "&gt;", "&gt;": "&lt;", "≤": "≥", "≥": "≤" }[ REL ]</var>
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19 </div>
5d9c4a2 @spicyj Add exercise -- linear inequalities
spicyj authored
20
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
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21 <div class="problems">
22 <div>
23 <p class="question">Solve for <code>x</code>:</p>
24 <div><code><var>A</var>x + <var>B</var> <var>REL</var> <var>C</var>x + <var>D</var></code></div>
5d9c4a2 @spicyj Add exercise -- linear inequalities
spicyj authored
25
0f0c630 @cbhl Clean up the exercise files using the new cleaning utility. (II)
cbhl authored
26 <p class="solution" data-type="multiple">
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27 <code>x</code>
62dae32 @cbhl Clean up the exercise files using the new cleaning utility. (IV)
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28 <span class="sol" data-choices="['', '&lt;', '&gt;', '≤', '≥']" data-type="list">
e9807ff @jeresig Clean up the exercise files using the new cleaning utility.
jeresig authored
29 <var>A - C &gt; 0 ? REL : FREL</var>
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30 </span>
31 <span class="sol"><var>( D - B ) / ( A - C )</var></span></p>
32 </div>
33 </div>
5d9c4a2 @spicyj Add exercise -- linear inequalities
spicyj authored
34
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
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35 <div class="hints">
36 <div>
37 <p>Subtract <code><var>C</var>x</code> from both sides:</p>
38 <p><code>(<var>A</var>x + <var>B</var>) - <var>C</var>x <var>REL</var> (<var>C</var>x + <var>D</var>) - <var>C</var>x</code></p>
39 <p><code><var>A - C</var>x + <var>B</var> <var>REL</var> <var>D</var></code></p>
40 </div>
41 <div>
72429d8 @jeresig Re-run the exercises through the linter.
jeresig authored
42 <p data-if="B > 0">Subtract <code><var>abs(B)</var></code> from both sides:</p><p data-else="">Add <code><var>abs(B)</var></code> to both sides:</p>
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
43 <p><code>(<var>A - C</var>x + <var>B</var>) + <var>-B</var> <var>REL</var> <var>D</var> + <var>-B</var></code></p>
44 <p><code><var>A - C</var>x <var>REL</var> <var>D - B</var></code></p>
45 </div>
72429d8 @jeresig Re-run the exercises through the linter.
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46 <div data-if="A - C > 0">
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47 <div>
48 <p>Divide both sides by <code><var>A - C</var></code>. Because <code><var>A - C</var></code> is positive, the inequality sign <code><var>REL</var></code> should not be flipped.</p>
49 <p><code>\dfrac{<var>A - C</var>x}{<var>A - C</var>} <var>REL</var> \dfrac{<var>D - B</var>}{<var>A - C</var>}</code></p>
50 </div>
51 <div>
52 <p>Simplify.</p>
53 <p><code>x <var>REL</var> <var>SOLUTION</var></code></p>
54 </div>
55 </div>
e9807ff @jeresig Clean up the exercise files using the new cleaning utility.
jeresig authored
56 <div data-else="">
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57 <div>
58 <p>Divide both sides by <code><var>A - C</var></code>. Because <code><var>A - C</var></code> is negative, the inequality sign <code><var>REL</var></code> must be flipped to <code><var>FREL</var></code>.</p>
59 <p><code>\dfrac{<var>A - C</var>x}{<var>A - C</var>} <var>FREL</var> \dfrac{<var>D - B</var>}{<var>A - C</var>}</code></p>
60 </div>
61 <div>
62 <p>Simplify.</p>
63 <p><code>x <var>FREL</var> <var>SOLUTION</var></code></p>
64 </div>
65 </div>
66 </div>
67 </div>
cde9e9f @jeresig Re-run the exercises through the updated cleaner.
jeresig authored
68 </body>
69 </html>
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