Certainly! To solve the equation [tex]\( 13x = 52 \)[/tex], we'll go through the following steps:
1. Understanding the Equation:
The given equation is [tex]\( 13x = 52 \)[/tex]. This is a single-variable linear equation where we need to find the value of [tex]\( x \)[/tex] that satisfies this equation.
2. Isolate the Variable [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], we need to get rid of the coefficient 13 that is attached to [tex]\( x \)[/tex]. The most straightforward way to do this is by dividing both sides of the equation by 13.
3. Divide Both Sides by 13:
[tex]\[
\frac{13x}{13} = \frac{52}{13}
\][/tex]
4. Simplify:
Simplifying the left-hand side, the 13s cancel each other out, leaving:
[tex]\[
x = \frac{52}{13}
\][/tex]
5. Perform the Division:
[tex]\[
x = 4
\][/tex]
So, the solution to the equation [tex]\( 13x = 52 \)[/tex] is [tex]\( x = 4 \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{x=4}
\][/tex]
This corresponds to option C.
