Answer :
To solve the problem, we need to translate the given statement into a mathematical inequality. The statement is: "The difference of [tex]\( x \)[/tex] and [tex]\( 5y \)[/tex] is fewer than 83."
Here's how we can interpret and solve this:
1. Identify the Mathematical Expression:
- The phrase "the difference of [tex]\( x \)[/tex] and [tex]\( 5y \)[/tex]" refers to subtracting [tex]\( 5y \)[/tex] from [tex]\( x \)[/tex], which is expressed as [tex]\( x - 5y \)[/tex].
2. Translating the Phrase "Fewer Than":
- The words "fewer than" indicate a strict inequality "<" (less than).
3. Construct the Inequality:
- Combining the expression and the inequality, we get:
[tex]\[
x - 5y < 83
\][/tex]
4. Select the Correct Answer:
- We compare this inequality with the given options:
- [tex]\( x - 5y > 83 \)[/tex]
- [tex]\( 5y \geq -x + 83 \)[/tex]
- [tex]\( x - 5y < 83 \)[/tex]
- [tex]\( 5y \leq -x + 83 \)[/tex]
- Clearly, the option [tex]\( x - 5y < 83 \)[/tex] matches our translated inequality.
Therefore, the correct inequality that models the statement is [tex]\( x - 5y < 83 \)[/tex].
Here's how we can interpret and solve this:
1. Identify the Mathematical Expression:
- The phrase "the difference of [tex]\( x \)[/tex] and [tex]\( 5y \)[/tex]" refers to subtracting [tex]\( 5y \)[/tex] from [tex]\( x \)[/tex], which is expressed as [tex]\( x - 5y \)[/tex].
2. Translating the Phrase "Fewer Than":
- The words "fewer than" indicate a strict inequality "<" (less than).
3. Construct the Inequality:
- Combining the expression and the inequality, we get:
[tex]\[
x - 5y < 83
\][/tex]
4. Select the Correct Answer:
- We compare this inequality with the given options:
- [tex]\( x - 5y > 83 \)[/tex]
- [tex]\( 5y \geq -x + 83 \)[/tex]
- [tex]\( x - 5y < 83 \)[/tex]
- [tex]\( 5y \leq -x + 83 \)[/tex]
- Clearly, the option [tex]\( x - 5y < 83 \)[/tex] matches our translated inequality.
Therefore, the correct inequality that models the statement is [tex]\( x - 5y < 83 \)[/tex].
