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<!--replace-end-7--><!--replace-end-4--><!--replace-end-1--></head><body><div class="ui fluid container universe"><!--replace-start-2--><!--replace-start-3--><!--replace-start-6--><div class="ui text container" id="zettel-container" style="position: relative"><div class="zettel-view"><article class="ui raised attached segment zettel-content"><div class="pandoc"><h1 id="title-h1">Solving equations</h1><h2 id="use-inversion-of-operators">Use inversion of operators</h2><p>When solving equations we frequently make use of the <a href="Inversion%20of%20operators.md"> operator inversion rules</a> to find the solutions.</p><h3 id="example-inversion-of-addition">Example: inversion of addition</h3><p>For example, the equation <span class="math inline">\(9 = 3 + x\)</span> has the solution <span class="math inline">\(6\)</span> (<span class="math inline">\(x\)</span> is equal to <span class="math inline">\(6\)</span>). To arrive at this, we can use the inverse of the main operator in the equation (addition): <span class="math inline">\(9-3 = 6\)</span>.</p><h3 id="example-inversion-of-subtraction">Example: inversion of subtraction</h3><p>Now consider <span class="math inline">\(19 = x - 3\)</span>. The solution to this equation is <span class="math inline">\(22\)</span> (<span class="math inline">\(x\)</span> is equal to <span class="math inline">\(22\)</span>). To arrive at this, we can use the inverse of the main operator in the equation (subtraction): <span class="math inline">\(19 + 3 = 22\)</span>.</p><h3 id="example-inversion-of-division">Example: inversion of division</h3><p>The equation we want to solve: <span class="math display">$$\frac{x}{6} = 4$$</span></p><p>Now we invert it by multiplying the denominator by the quotient: <span class="math inline">\(6\cdot 4 = 24\)</span>. Therefore: <span class="math display">$$ \frac{24}{6} = 4$$</span> The solution is <span class="math inline">\(24\)</span></p><h3 id="example-inversion-of-multiplication">Example: inversion of multiplication</h3><p>The equation we want to solve: <span class="math display">$$4x = 36$$</span> Now we invert it by dividing the product by the coefficient: !Add link to ‘coefficient’</p><p><span class="math display">$$\frac{36}{4} = 9$$</span></p><p>Therefore the solution is <span class="math inline">\(9\)</span>: <span class="math display">$$ 4(9) = 36$$</span></p></div></article><nav class="ui attached segment deemphasized bottomPane" id="neuron-tags-pane"><div><span class="ui basic label zettel-tag" title="Tag">algebra</span></div></nav><nav class="ui bottom attached icon compact inverted menu blue" id="neuron-nav-bar"><!--replace-start-9--><!--replace-end-9--><a class="right item" href="impulse.html" title="Open Impulse"><i class="wave square icon"></i></a></nav></div></div><!--replace-end-6--><!--replace-end-3--><!--replace-end-2--><div class="ui center aligned container footer-version"><div class="ui tiny image"><a href="https://neuron.zettel.page"><img alt="logo" src="https://raw.githubusercontent.com/srid/neuron/master/assets/neuron.svg" title="Generated by Neuron 1.9.35.3" /></a></div></div></div></body></html> |