- Identify the linear equation \(6x + 2 = 20\).
- Subtract 2 from both sides to get \(6x = 18\).
- Divide both sides by 6 to isolate \(x\).
- The solution is \(x = \boxed{3}\).
Explanation
- Problem Analysis
The given equation is a linear equation in one variable: \(6x + 2 = 20\). Our goal is to isolate the variable \(x\) to find its value. The equation contains a term with \(x\) (\(6x\)) and a constant (\(2\)) on the left-hand side, and a constant (\(20\)) on the right-hand side.
- Isolating the Variable Term
To isolate the term with \(x\), we first subtract the constant term \(2\) from both sides of the equation:
\[6x + 2 - 2 = 20 - 2\]
\[6x = 18\]
- Solving for x
Now, we solve for \(x\) by dividing both sides of the equation by the coefficient of \(x\), which is \(6\):
\[\frac{6x}{6} = \frac{18}{6}\]
\[x = 3\]
Thus, the value of \(x\) that satisfies the original equation is \(3\).
Examples
Linear equations like \(6x + 2 = 20\) are fundamental in everyday scenarios where costs or quantities are calculated. For instance, if you are buying items where you pay a fixed shipping fee of \$2 and each item costs \$6, and your total bill is \$20, you can use this equation to determine how many items you purchased. By solving for \(x\), you find that you bought 3 items. Such calculations are useful in budgeting, shopping, and planning resources efficiently.