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<!DOCTYPE html>
<html data-require="math math-format expressions">
<head>
<meta charset="UTF-8" />
<title>One-step equations</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="LETTERS">"abkmnpvx"</var>
<var id="X">LETTERS.charAt( randRange( 0, LETTERS.length - 1 ) )</var>
</div>
<div class="problems">
<div id="add" data-weight="4">
<div class="vars" data-ensure="Y !== Z">
<var id="INDEX">randRange( 0, 3 )</var>
<var id="Y">randRangeNonZero( -30, 30 )</var>
<var id="Z">randRangeNonZero( -30, 30 )</var>
<var id="Y_SIGN">Y > 0 ? "-" : "+"</var>
<var id="LEFT">[expr( ["+", X, Y] ), expr( ["+", Y, X] ), Z, Z][INDEX]</var>
<var id="RIGHT">[Z, Z, expr( ["+", X, Y] ), expr( ["+", Y, X] )][INDEX]</var>
</div>
<p class="question">Solve for <var>X</var>.</p>
<p><code>\large{<var>LEFT</var> = <var>RIGHT</var>}</code></p>
<div class="solution" data-type="rational"><var>Z - Y</var></div>
<div class="hints">
<div>
<p><span data-if="Y &lt; 0">Add <var>Y * -1</var> to</span><span data-else>Subtract <var>Y</var> from</span> both sides.</p>
<p data-if="INDEX &lt; 2"><code>\large{<var>X</var> = <var>RIGHT</var>\color{blue}{<var>Y_SIGN</var><var>abs( Y )</var>}}</code></p>
<p data-else><code>\large{<var>LEFT</var>\color{blue}{<var>Y_SIGN</var><var>abs( Y )</var>} = <var>X</var>}</code></p>
</div>
<div>
<p>Simplify.</p>
<p><code>\large{<var>X</var> = <var>Z - Y</var>}</code></p>
</div>
</div>
</div>
<div id="multiply" data-weight="2">
<div class="vars">
<var id="INDEX">randRange( 0, 1 )</var>
<var id="Y">randRange( 2, 20 ) * randRangeNonZero( -1, 1 )</var>
<var id="Z">randRange( 2, 20 - abs( Y ) + 5 ) * randRangeNonZero( -1, 1 ) * Y</var>
<var id="Y_SIGN">Y * Z > 0 ? "" : "-"</var>
<var id="LEFT">[expr( ["*", Y, X] ), Z][INDEX]</var>
<var id="RIGHT">[Z, expr( ["*", Y, X] )][INDEX]</var>
</div>
<p class="question">Solve for <var>X</var>.</p>
<p><code>\large{<var>LEFT</var> = <var>RIGHT</var>}</code></p>
<div class="solution" data-type="rational"><var>Z / Y</var></div>
<div class="hints">
<div data-if="INDEX === 0">
<p>Divide both sides by <var>Y</var>.</p>
<p data-if="Y &lt; 0 && Z &lt; 0"><code>\large{<var>X</var> = \dfrac{<var>Z</var>}{\color{blue}{<var>Y</var>}}}</code></p>
<p data-else><code>\large{<var>X</var> = <span data-if="Y &lt; 0">\color{blue}{<var>Y_SIGN</var>}</span><span data-else><var>Y_SIGN</var></span>\dfrac{<var>abs( Z )</var>}{\color{blue}{<var>abs( Y )</var>}}}</code></p>
</div>
<div data-else>
<p>Divide both sides by <var>Y</var>.</p>
<p data-if="Y &lt; 0 && Z &lt; 0"><code>\large{\dfrac{<var>Z</var>}{\color{blue}{<var>Y</var>}} = <var>X</var>}</code></p>
<p data-else><code>\large{<span data-if="Y &lt; 0">\color{blue}{<var>Y_SIGN</var>}</span><span data-else><var>Y_SIGN</var></span>\dfrac{<var>abs( Z )</var>}{\color{blue}{<var>abs( Y )</var>}} = <var>X</var>}</code></p>
</div>
<div>
<p>Simplify.</p>
<p><code>\large{<var>X</var> = <var>Z / Y</var>}</code></p>
</div>
</div>
</div>
<div id="divide" data-weight="1">
<div class="vars">
<var id="INDEX">randRange( 0, 1 )</var>
<var id="Y">randRange( 2, 20 )</var>
<var id="Z">randRange( 2, 20 - abs( Y ) + 5 ) * randRangeNonZero( -1, 1 )</var>
</div>
<p class="problem"><b>Solve for <var>X</var>.</b></p>
<p class="question"><code>\large{\dfrac{<var>X</var>}{<var>Y</var>} = <var>Z</var>}</code></p>
<div class="solution" data-type="rational"><var>Z * Y</var></div>
<div class="hints">
<div>
<p>Multiply both sides by <var>Y</var>.</p>
<p><code>\large{<var>X</var> = <var>Z</var> \cdot {\color{blue}{<var>Y</var>}}}</code></p>
</div>
<div>
<p>Simplify.</p>
<p><code>\large{<var>X</var> = <var>Z * Y</var>}</code></p>
</div>
</div>
</div>
<div id="divide-right" data-type="divide" data-weight="1">
<p class="question"><code>\large{<var>Z</var> = \dfrac{<var>X</var>}{<var>Y</var>}}</code></p>
<div class="hints">
<div>
<p>Multiply both sides by <var>Y</var>.</p>
<p><code>\large{<var>Z</var> \cdot {\color{blue}{<var>Y</var>}} = <var>X</var>}</code></p>
</div>
<div>
<p>Simplify.</p>
<p><code>\large{<var>X</var> = <var>Z * Y</var>}</code></p>
</div>
</div>
</div>
</div>
</div>
</body>
</html>
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