Solving a Linear Equation with Distributed Terms
<p>The given equation is:</p>
<p>\(\frac{1}{2} (90 + 22x - 10) \cdot 120 = 14,400\).</p>
<p>To solve for \(x\), first simplify the equation:</p>
<p>Multiply 120 by each term inside the parentheses:</p>
<p>\(\frac{1}{2} (120 \cdot 80 + 120 \cdot 22x) = 14,400\)</p>
<p>\(\frac{1}{2} (9600 + 2640x) = 14,400\)</p>
<p>Multiply both sides by 2 to eliminate the fraction:</p>
<p>\(9600 + 2640x = 28,800\)</p>
<p>Subtract 9600 from both sides to isolate the \(x\) term:</p>
<p>\(2640x = 28,800 - 9600\)</p>
<p>\(2640x = 19,200\)</p>
<p>Divide both sides by 2640 to solve for \(x\):</p>
<p>\(x = \frac{19,200}{2640}\)</p>
<p>\(x = 7.2727...\)</p>
<p>As an exact fraction, \(x\) equals:</p>
<p>\(x = \frac{7}{22}\)</p>
