What is the solution to this equation?

[tex]\[ 13x = 52 \][/tex]

A. [tex]\( x = -65 \)[/tex]
B. [tex]\( x = -4 \)[/tex]
C. [tex]\( x = 4 \)[/tex]
D. [tex]\( x = 65 \)[/tex]



Answer :

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.