* Solve the following equation for \( x \). \[ a x-2=20 \] A \( x=\frac{22}{a} \) B \( x=\frac{a}{22} \) C \( x=\frac{20-a}{2} \) D \( x=\frac{18}{a} \)

To solve the equation \( a x - 2 = 20 \), we start by isolating the term containing \( x \). Add 2 to both sides: \[ a x = 22 \] Next, we divide both sides by \( a \) (assuming \( a \neq 0 \)): \[ x = \frac{22}{a} \] Therefore, the correct answer is A \( x = \frac{22}{a} \). Now, let's add some engaging facts! Mathematics has a rich history: the concept of algebra dates back to ancient civilizations, including the Babylonians and Greeks, who used geometric methods to solve equations without the symbolic representation we have today. The term "algebra" itself derives from the Arabic word "al-jabr," meaning "reunion of broken parts." In the real world, the ability to solve equations like \( a x - 2 = 20 \) is crucial. For example, if \( a \) represented the rate of pay and \( x \) the hours worked, finding \( x \) helps someone budget their time effectively. You might consider how that applies to your own life—whether balancing study time or budgeting weekend plans!