- Start with the equation \(x + 8 = 1\).
- Isolate the variable \(x\) by subtracting \(8\) from both sides of the equation.
- Calculate the result: \(x = 1 - 8 = -7\).
- The final value of \(x\) is \(\boxed{-7}\).
Explanation
- Problem Analysis
The given equation is \(x + 8 = 1\). We are asked to find the value of the variable \(x\). This is a simple linear equation where we need to isolate the unknown variable \(x\) to determine its value. The equation involves the addition of the constant \(8\) to \(x\), so we need to perform the inverse operation, which is subtraction, to isolate \(x\).
- Solving the Equation
To isolate \(x\), we subtract \(8\) from both sides of the equation.
Starting with:
\[x + 8 = 1\]
Subtracting \(8\) from both sides:
\[x + 8 - 8 = 1 - 8\]
This simplifies to:
\[x = 1 - 8\]
Performing the subtraction:
\[x = -7\]
Thus, the value of \(x\) that satisfies the equation is \(-7\).
Examples
Suppose you are playing a game where your score is currently \(x\). You gain \(8\) points, bringing your total score to \(1\). To find your starting score \(x\), you subtract the \(8\) points you gained from your final total: \(x + 8 = 1 \implies x = 1 - 8 = -7\). This shows how basic linear algebra helps track changes in values or balances in everyday scenarios.