To address the given statement "The product of 18 and a number is greater than 2," we first need to write it as a mathematical expression and then solve for the number.
1. Step 1: Write the mathematical expression:
The statement "The product of 18 and a number" can be represented as [tex]\(18 \cdot x\)[/tex], where [tex]\(x\)[/tex] is the unknown number.
The phrase "is greater than 2" translates to the inequality symbol [tex]\(>\)[/tex].
Hence, the mathematical expression for the given statement is:
[tex]\[
18x > 2
\][/tex]
2. Step 2: Solve the inequality:
To solve for [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex] on one side of the inequality. This can be done by dividing both sides of the inequality by 18:
[tex]\[
18x > 2
\][/tex]
[tex]\[
x > \frac{2}{18}
\][/tex]
3. Step 3: Simplify the fraction:
Simplifying [tex]\(\frac{2}{18}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor (which is 2), we get:
[tex]\[
x > \frac{1}{9}
\][/tex]
Therefore, the complete inequality solution is:
[tex]\[
x > \frac{1}{9}
\][/tex]
Among the given options, the correct one is:
\[
18 x > 2; \, x > \frac{1}{9}
\
