To address the given statement, "The product of a number and 7 is no more than 56," we need to formulate an inequality that correctly represents this situation.
Let's break down the statement into mathematical terms:
1. Identify the product of a number and 7:
- Let the number be denoted as [tex]\( n \)[/tex].
- The product of this number and 7 is expressed as [tex]\( 7n \)[/tex].
2. Interpret the phrase "no more than 56":
- "No more than" means the quantity is either less than or equal to 56.
- Mathematically, this is represented by the symbol [tex]\( \leq \)[/tex].
Combining these two parts, the correct inequality would be:
[tex]\[ 7n \leq 56 \][/tex]
Now, let's examine the provided options to find the one that matches our derived inequality:
a. [tex]\( 7n \leq 56 \)[/tex]
b. [tex]\( 7n < 56 \)[/tex]
c. [tex]\( 7n > 56 \)[/tex]
d. [tex]\( 7 + n \leq 56 \)[/tex]
Clearly, the option that correctly represents the statement "The product of a number and 7 is no more than 56" is:
Option a. [tex]\( 7n \leq 56 \)[/tex]
