To determine the correct equation that could be solved to find the value of the smaller number [tex]\( x \)[/tex], given that the product of two numbers [tex]\( x \)[/tex] and [tex]\( x + 3 \)[/tex] is 550, let's follow these steps:
1. Understand the given information and set up the equation:
- The problem states that the product of the numbers [tex]\( x \)[/tex] and [tex]\( x + 3 \)[/tex] is 550.
- Therefore, the equation representing this situation is:
[tex]\[
x(x + 3) = 550
\][/tex]
2. Expand and simplify the equation:
- Multiply [tex]\( x \)[/tex] by [tex]\( x + 3 \)[/tex]:
[tex]\[
x \cdot (x + 3) = 550
\][/tex]
- This simplifies to:
[tex]\[
x^2 + 3x = 550
\][/tex]
3. Identify the correct answer choice:
- We look at our simplified equation [tex]\( x^2 + 3x = 550 \)[/tex] and compare it to the given answer choices:
- A. [tex]\( 3x + 3 = 550 \)[/tex]
- B. [tex]\( 3x^2 = 500 \)[/tex]
- C. [tex]\( x^2 + 3 = 550 \)[/tex]
- D. [tex]\( x^2 + 3x = 550 \)[/tex]
- The equation [tex]\( x^2 + 3x = 550 \)[/tex] corresponds to option D.
Therefore, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
