To center a mirror on a wall, we need to determine the distance [tex]\( x \)[/tex] on each side of the mirror. Let's break this down step-by-step:
1. Understand the total width of the wall and the mirror:
- The width of the mirror is [tex]\( 4' \)[/tex].
- The width of the wall is [tex]\( 20' \)[/tex].
2. Visualize the scenario:
- When the mirror is centered, there will be a section of the wall on each side of the mirror.
- Let's denote the distance on each side of the mirror as [tex]\( x \)[/tex].
3. Set up the equation:
- If the mirror width is [tex]\( 4' \)[/tex], and there is [tex]\( x \)[/tex] feet of wall on each side of the mirror, we can represent the total width of the wall as the sum of these parts.
- The total width of the wall includes the width of the mirror and the distances on both sides:
[tex]\[
x + \text{mirror width} + x = \text{wall width}
\][/tex]
4. Plug in the specific values:
- The mirror width is [tex]\( 4' \)[/tex], and the wall width is [tex]\( 20' \)[/tex].
- So, the equation becomes:
[tex]\[
x + 4 + x = 20
\][/tex]
5. Simplify the equation:
- Combine like terms:
[tex]\[
2x + 4 = 20
\][/tex]
Thus, the correct equation that helps determine the distance [tex]\( x \)[/tex] on each side of the mirror is:
[tex]\[ \boxed{x + 4 + x = 20} \][/tex]
So, the correct choice is:
[tex]\[
(A) \, x + 4 + x = 20
\][/tex]
