You can quickly verify your answer by substituting it back into the original equation. For \(x=3\), the equation becomes \(5(3) - 8 = 15 - 8 = 7\). Since this is true, the answer is correct.
Step 1: Understanding the Concept:
This is a two-step linear equation. The goal is to isolate the variable \(x\) using algebraic manipulations. Step 2: Detailed Explanation:
The given equation is:
\[ 5x - 8 = 7 \]
First, add 8 to both sides of the equation to isolate the term with \(x\):
\[ 5x = 7 + 8 \]
\[ 5x = 15 \]
Next, divide both sides by 5 to solve for \(x\):
\[ x = \frac{15}{5} \]
\[ x = 3 \]
Step 3: Final Answer:
The value of \(x\) is 3. This corresponds to option (C).