To solve the problem, let's break it down step-by-step.
The problem states that the product of two numbers, [tex]\( x \)[/tex] and [tex]\( x + 3 \)[/tex], is 550.
1. The first number is [tex]\( x \)[/tex].
2. The second number is [tex]\( x + 3 \)[/tex].
We can represent the product of these two numbers as:
[tex]\[ x \cdot (x + 3) = 550 \][/tex]
To find the correct equation that represents the given condition, we need to rewrite the product in a simplified form:
3. Distribute [tex]\( x \)[/tex] into [tex]\( (x + 3) \)[/tex]:
[tex]\[ x^2 + 3x = 550 \][/tex]
So, the equation that could be solved to find the value of the smaller number [tex]\( x \)[/tex] is:
[tex]\[ x^2 + 3x = 550 \][/tex]
Therefore, the correct answer is:
D. [tex]\( x^2 + 3x = 550 \)[/tex]
