To write an inequality from the statement "The sum of a number and 9 is less than 100," we need to translate the words into a mathematical expression.
1. Let's denote the unknown number as [tex]\( n \)[/tex].
2. The phrase "The sum of a number and 9" translates to [tex]\( n + 9 \)[/tex].
3. The phrase "is less than" translates to the inequality symbol [tex]\( < \)[/tex].
4. The number 100 remains 100 in the inequality.
Combining these elements, the statement "The sum of a number and 9 is less than 100" translates to the inequality:
[tex]\[ n + 9 < 100 \][/tex]
Now, let's look at the given options and select the correct one:
a. [tex]\( n + 9 < 100 \)[/tex]
b. [tex]\( n - 9 > 100 \)[/tex]
c. [tex]\( 9n > 100 \)[/tex]
d. [tex]\( n < 9 + 100 \)[/tex]
The correct inequality is:
[tex]\[ n + 9 < 100 \][/tex]
So, the correct answer is:
a. [tex]\( n + 9 < 100 \)[/tex]
