Let's break down the given information and find the correct equation and second number step-by-step.
We are given:
- The product of two numbers is 21.
- The first number is -3.
We need to identify the correct equation and find the second number.
1. Identify the correct equation:
- The product of two numbers means we multiply the first number by the second number to get 21.
- Let the second number be [tex]\( x \)[/tex].
- Since the first number is -3, our equation becomes:
[tex]\[
-3 \cdot x = 21
\][/tex]
Reviewing the options:
- Option A: [tex]\( x - 3 = 21 \)[/tex] (This is incorrect because it represents a different operation, subtraction, rather than multiplication).
- Option B: [tex]\( 3x = 21 \)[/tex] (This is incorrect because the first number should be -3, not 3).
- Option C: [tex]\( -3x = 21 \)[/tex] (This is the correct equation as it correctly represents the multiplication of -3 and [tex]\( x \)[/tex] yielding 21).
- Option D: [tex]\( -3 + x = 21 \)[/tex] (This is incorrect because it represents an addition operation, rather than multiplication).
Therefore, the correct equation is [tex]\( -3x = 21 \)[/tex].
2. Solve for the second number:
- We solve the equation [tex]\( -3x = 21 \)[/tex] for [tex]\( x \)[/tex].
[tex]\[
-3x = 21
\][/tex]
[tex]\[
x = \frac{21}{-3}
\][/tex]
[tex]\[
x = -7
\][/tex]
So, the second number is [tex]\( -7 \)[/tex].
Thus, the correct answer is:
C. The equation that represents this situation is [tex]\( -3x = 21 \)[/tex]. The second number is -7.
