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<h4>Verify a Solution of an Equation</h4>
<p>Solving an <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">equation</span>
is like discovering the answer to a puzzle. The purpose in solving an equation is to find the value or values of the
<span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">variable</span> that make
each side of the equation the same so that we end up with a true statement. Any value of the variable that makes the
equation true is called a <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">solution of an equation</span>. It is the answer to the puzzle!
</p>
<p>How to determine whether a number is a solution to an equation:</p>
<p><strong>STEP 1:</strong> Substitute the number in for the variable in the equation.</p>
<p><strong>Step 2 </strong> -Simplify the expressions on both sides of the equation</p>
<p><strong>Step 3 </strong> -Determine whether the resulting equation is true (the left side is equal to the right
side).<br>
If it is true, the number is a solution.<br>
If it is not true, the number is not a solution.</p>
<p>For example, the equation \( 2l+2w=72 \) represents the relationship between the length, \( l \), and the width,
\( w \), of a rectangle that has a perimeter of 72 units. If we know that the length is 15 units, what is the
value of the width?
</p>
<p><strong>STEP 1:</strong> Substitute the number in for the variable in the equation.</p>
<p>\( 2(15)+2w=72 \)</p>
<p>This is an equation in one variable because \(w\) is the only quantity that we don't know. To solve this equation
means to find a value of \(w\) that makes the equation true.</p>
<p><strong>Step 2 </strong> -Simplify the expressions on both sides of the equation<br>
In this case, 21 is the solution because substituting 21 for \( w \) in the equation results in a true statement.
</p>
<p>\( 2(15)+2w=72 \)</p>
<p>\( 2(15)+2(21)=72 \)</p>
<p>\( 30+42=72 \)</p>
<p><strong>Step 3 </strong> -Determine whether the resulting equation is true (the left side is equal to the right
side).<br>
If it is true, the number is a solution.<br>
If it is not true, the number is not a solution.</p>
<p>\( 72=72 \)</p>
<h4>Try It: Verify a Solution of an Equation</h4>
<p>The equation \(2l + 2w = 48\) represents the perimeter of a rectangle.
</p>
<br>
<!--Q1 -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="05234c74-c9b8-497d-ab19-62c5afe0fec1" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>If the width of the rectangle is 10, what is the new equation?
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(2l + 2(10) = 48\) or \(2l + 20 = 48\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="059b292f-c9cf-40da-8ceb-2e04bd7761f1" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q2-->
<div class="os-raise-ib-pset-problem" data-content-id="5d732f70-e3cf-4cbc-ad12-955ef4384966" data-problem-comparator="integer" data-problem-type="input" data-solution="14">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li>What is the length of the rectangle that has a width of 10?
</li>
</ol>
<p>Enter your length measurement here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 14</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is 14.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<!--Q3 -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="2854919c-ff24-4cb2-9755-af70d7fe693e" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Verify the solution.
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your verification here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>To verify the solution, substitute \(w = 10\) and \(l = 14\) into \(2l + 2w = 48\).<br>
\(2(14) + 2(10) = 48\)<br>
\(28 + 20 = 48\)<br>
\(48 = 48\) is a true statement, so the solution works!
</p>
</div>
</div>
<!--Interaction End -->
<br>