Question - Solving a Linear Equation with Distributed Terms

The given equation is:

\(\frac{1}{2} (90 + 22x - 10) \cdot 120 = 14,400\).

To solve for \(x\), first simplify the equation:

Multiply 120 by each term inside the parentheses:

\(\frac{1}{2} (120 \cdot 80 + 120 \cdot 22x) = 14,400\)

\(\frac{1}{2} (9600 + 2640x) = 14,400\)

Multiply both sides by 2 to eliminate the fraction:

\(9600 + 2640x = 28,800\)

Subtract 9600 from both sides to isolate the \(x\) term:

\(2640x = 28,800 - 9600\)

\(2640x = 19,200\)

Divide both sides by 2640 to solve for \(x\):

\(x = \frac{19,200}{2640}\)

\(x = 7.2727...\)

As an exact fraction, \(x\) equals:

\(x = \frac{7}{22}\)