To solve the problem, let's break it down step-by-step.
Given: "Two less than the product of a number and three". We are asked to evaluate this expression for [tex]\( f = 4.5 \)[/tex].
Using the key words from the table:
- "Two" is replaced with 2.
- "Less than" translates to subtraction, which we indicate with the minus sign (-).
- "Product" implies multiplication, indicated by the multiplication sign (×).
- "A number" is represented by [tex]\( f \)[/tex].
- "Three" is replaced with 3.
### Writing the Expressions
We have three possible expressions provided:
1. [tex]\( 2 - 3f \)[/tex]
2. [tex]\( 3f - 2 \)[/tex]
3. [tex]\( 2f - 3 \)[/tex]
Now, let's evaluate each of these expressions for [tex]\( f = 4.5 \)[/tex].
#### 1. Expression: [tex]\( 2 - 3f \)[/tex]
Substitute [tex]\( f = 4.5 \)[/tex] into the expression:
[tex]\[ 2 - 3 \times 4.5 \][/tex]
[tex]\[ 2 - 13.5 \][/tex]
[tex]\[ -11.5 \][/tex]
#### 2. Expression: [tex]\( 3f - 2 \)[/tex]
Substitute [tex]\( f = 4.5 \)[/tex] into the expression:
[tex]\[ 3 \times 4.5 - 2 \][/tex]
[tex]\[ 13.5 - 2 \][/tex]
[tex]\[ 11.5 \][/tex]
#### 3. Expression: [tex]\( 2f - 3 \)[/tex]
Substitute [tex]\( f = 4.5 \)[/tex] into the expression:
[tex]\[ 2 \times 4.5 - 3 \][/tex]
[tex]\[ 9 - 3 \][/tex]
[tex]\[ 6 \][/tex]
### Conclusion
After evaluating the expressions, we found the following results:
- For [tex]\( 2 - 3f \)[/tex], the value is [tex]\(-11.5\)[/tex].
- For [tex]\( 3f - 2 \)[/tex], the value is [tex]\(11.5\)[/tex].
- For [tex]\( 2f - 3 \)[/tex], the value is [tex]\(6\)[/tex].
Therefore, among the options given:
- The value when [tex]\( f = 4.5 \)[/tex] is not [tex]\(6.75\)[/tex].
- The value when [tex]\( f = 4.5 \)[/tex] is [tex]\(6\)[/tex], which corresponds to the expression [tex]\( 2f - 3 \)[/tex].
- The value when [tex]\( f = 4.5 \)[/tex] is [tex]\(11.5\)[/tex], which corresponds to the expression [tex]\( 3f - 2 \)[/tex].
Based on these computations, the correct evaluations are when [tex]\( f = 4.5 \)[/tex]:
- [tex]\( 6 \)[/tex], for the expression [tex]\( 2f - 3 \)[/tex].
- [tex]\( 11.5 \)[/tex], for the expression [tex]\( 3f - 2 \)[/tex].
