- To isolate the variable \(x\), we identify the inverse operation of division by 3, which is multiplication by 3.
- We multiply both sides of the equation by 3: \(\frac{x}{3} \times 3 = -8 \times 3\).
- Simplifying the expression leads to the final result, \(x = -24\).
- Final Answer: \(\boxed{-24}\)
Explanation
- Understanding the Problem
We are tasked with solving the equation \(\frac{x}{3} = -8\) for the variable \(x\). This is a simple linear equation where the variable is divided by 3. To find the value of \(x\), we need to perform an operation that isolates \(x\) on one side of the equation.
- Isolating the Variable x
To isolate \(x\), we must reverse the division by 3. The inverse operation to division is multiplication. Therefore, we multiply both sides of the equation by 3:
\[\frac{x}{3} \times 3 = -8 \times 3\]
- Final Solution
Simplifying both sides of the equation, we get:
\[x = -24\]
Thus, the solution to the equation is \(x = -24\).
Examples
In real life, this simple algebraic manipulation is used whenever you need to find a total value from a fractional part. For example, if you know that one-third of a budget allocation for a project is \(\$-800\) (in thousands, so -8 units), you can determine the total budget by multiplying by 3: \(\frac{x}{3} = -8 \implies x = -24\). Such calculations are foundational for budgeting, scaling recipes, or determining total distances based on segments.