The problem is to simplify the expression $\sqrt{169x^2}$, assuming that the variable $x$ can be any positive or negative real number.

1. Problem Description

The problem is to simplify the expression $\sqrt{169x^2}$, assuming that the variable $x$ can be any positive or negative real number.

2. Solution Steps

We need to simplify $\sqrt{169x^2}$.

Since the square root of a product is the product of the square roots, we can rewrite the expression as $\sqrt{169} \cdot \sqrt{x^2}$.

We know that $\sqrt{169} = 13$, since $13 \cdot 13 = 169$.

Since $x$ can be either positive or negative, $\sqrt{x^2}$ is equal to the absolute value of $x$, which is written as $|x|$.

Therefore, $\sqrt{169x^2} = \sqrt{169} \cdot \sqrt{x^2} = 13|x|$.

3. Final Answer

$13|x|$