ba75e12d-6755-4b0f-9c50-fe13da520015.html

<h3>Solve a Formula for a Specific Variable</h3>
<p>Solving for a variable in a formula is actually finding equivalent equations.</p>
<p><span>To solve a formula for a specific variable means to isolate that variable on one side of the equals sign with a
    coefficient of 1. All other variables and constants are on the other side of the equals sign. To see how to solve a
    formula for a specific variable, we will start with the distance, rate and time formula.</span><br></p>
<p><strong>Example 1</strong><br>
  Solve the formula \(d=rt\) for \(t\) when \(d=520\) and \(r=65\).</p>
<br>
<p><strong>Step 1: </strong>Write the formula.<br>
  \(d=rt\)</p>
<p><strong>Step 2: </strong>Substitute.<br>
  \(520=65t\)</p>
<p><strong>STEP 3:</strong> Divide, to isolate \(t\).<br>
  \(\frac{520}{65}=\frac{65t}{65}\)</p>
<p><strong>Step 4: </strong>Simplify.<br>
  \(t = 8\)</p>
<br>
<p><strong>Example 2</strong><br>
  Solve the formula \(d=rt\) for \(t\).</p>
<p><strong>STEP 1:</strong> Write the formula.<br>
  \(d=rt\)</p>
<p><strong>STEP 2:</strong> Substitute.<br>
  (step not needed)</p>
<p><strong>Step 3: </strong>Divide, to isolate \(t\).<br>
  \(\frac{d}{r}=\frac{rt}{r}\)</p>
<p><strong>STEP 4:</strong> Simplify.<br>
  \(\frac{d}{r}=t\)</p>
<br>
<p><strong>Example 3</strong><br>
  Solve the formula \(A=\frac{1}{2}bh\) for \(h\), when \(A=90\) and \(b = 15\).</p>
<p><strong>STEP 1:</strong> Write the formula.<br>
  \(A=\frac{1}{2}bh\)</p>
<p><strong>STEP 2:</strong> Substitute.<br>
  \(90=\frac{1}{2}(15)h\)</p>
<p><strong>Step 3</strong>: Multiply to clear the fraction.<br>
  \(2 \times 90=2 \times \frac{1}{2}(15)h\)</p>
<p><strong>STEP 4:</strong> Simplify.<br>
  \(180=15h\)</p>
<p><strong>STEP 5:</strong> Solve for \(h\).<br>
  \(12=h\)
</p><br>
<p><strong>Example 4</strong><br>
  Solve the formula \(A=\frac{1}{2}bh\) for \(h\).</p>
<p><strong>STEP 1:</strong> Write the formula.<br>
  \(A=\frac{1}{2}bh\)</p>
<p><strong>STEP 2:</strong> Substitute.<br>
  (step not needed)</p>
<p><strong>STEP 3:</strong> Multiply to clear the fraction.<br>
  \(2 \times A=2 \times \frac{1}{2}bh\)</p>
<p><strong>Step 4: </strong>Simplify.<br>
  \(2A=bh\)</p>
<p><strong>STEP 5:</strong> Solve for \(h\).<br>
  \(\frac{2A}{b}=h\)</p><br>
<p><strong>Example 5</strong><br>
  Solve the formula \(3x+2y=18\) for \(y\) when \(x = 4\).</p>
<p>Step 1: Write the formula.<br>
  \(3x+2y=18\)</p>
<p><strong>STEP 2:</strong> Substitute.<br>
  \(3(4)+2y=18\)</p>
<p><strong>STEP 3:</strong> Simplify.<br>
  \(12+2y=18\)</p>
<p><strong>STEP 4:</strong> Isolate the \(y\)-term using subtraction.<br>
  \(12-12+2y=18-12\)</p>
<p><strong>STEP 5:</strong> Simplify.<br>
  \(2y=6\)</p>
<p><strong>Step 6: </strong>Divide.<br>
  \(\frac{2y}{2}=\frac{6}{2}\)</p>
<p><strong>STEP 7:</strong> Simplify.<br>
  \(y =3\)</p><br>
<p><strong>Example 6</strong><br>
  Solve the formula \(3x+2y=18\) for \(y\).</p>
<p><strong>Step 1: </strong>Write the formula.<br>
  \(3x+2y=18\)</p>
<p><strong>STEP 2:</strong> Substitute.<br>
  (step not needed)</p>
<p><strong>STEP 3:</strong> Simplify.<br>
  (step not needed)</p>
<p><strong>STEP 4:</strong> Isolate the \(y\)-term using subtraction.<br>
  \(3x-3x+2y=18-3x\)</p>
<p><strong>Step 5: </strong>Simplify.<br>
  \(2y =18-3x\)</p>
<p><strong>Step 6: </strong>Divide.<br>
  \(\frac{2y}{2}=\frac{18-3}{x2}\)</p>
<p><strong>STEP 7:</strong> Simplify.<br>
  \(y=-\frac{3}{2}x+9\) </p><br>
<h4>Try It: Solve a Formula for a Specific
  Variable </h4>
<!--Q#-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="5858107b-53db-4342-8c36-9b21bd6d1fa9" data-fire-event="eventShow" data-schema-version="1.0">
  <div class="os-raise-ib-input-content">
    <p>Solve \( 2x - 4y = 20\) for \(x \). </p>
  </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>Here is how to solve this equation for \(x\) by isolating:</p>
    <p><strong>STEP 1:</strong> Use inverse operations to bring the \(y\) term to the right side of the equation by adding
      4y.<br>
      \(2x-4y+4y=20+4y\)
    </p>
    <p><strong>STEP 2:</strong> Simplify.<br>
      \(2x=20+4y\)
    </p>
    <p><strong>STEP 3:</strong> Divide both sides by 2.<br>
      \(\frac{2x}{2}=\frac{20+4y}{2}\)
    </p>
    <p><strong>STEP 4:</strong> Simplify.<br>
      \(x=10+2y\)</p>
  </div>
</div>
<!--Interaction End -->
</br></br></br>