Let's break down the problem step by step to understand which statements are true about the expression "a number, [tex]\( n \)[/tex], decreased by thirty-one," and its evaluation when [tex]\( n = 29 \)[/tex].
### Step 1: Write the Expression
The expression for "a number, [tex]\( n \)[/tex], decreased by thirty-one" is:
[tex]\[ n - 31 \][/tex]
### Step 2: Evaluate the Expression with [tex]\( n = 29 \)[/tex]
Next, we substitute [tex]\( n = 29 \)[/tex] into the expression:
[tex]\[ n - 31 \][/tex]
[tex]\[ 29 - 31 \][/tex]
[tex]\[ -2 \][/tex]
### Step 3: Analyze the Statements
1. The correct expression is [tex]\( 31 - n \)[/tex].
- This statement is false. The correct expression is [tex]\( n - 31 \)[/tex], not [tex]\( 31 - n \)[/tex].
2. This is a subtraction expression.
- This statement is true. The expression involves subtraction (reducing [tex]\( n \)[/tex] by 31).
3. This is an addition expression.
- This statement is false. The expression involves subtraction, not addition.
4. To evaluate, substitute 29 for the variable in the expression.
- This statement is true. In order to evaluate the expression for [tex]\( n = 29 \)[/tex], we substitute 29 for [tex]\( n \)[/tex].
5. To evaluate, substitute 31 for the variable in the equation.
- This statement is false. The variable in the expression is [tex]\( n \)[/tex], and we substitute 29 for [tex]\( n \)[/tex], not 31.
6. To evaluate the expression, add 31 to 29.
- This statement is false. To evaluate the expression, we subtract 31 from 29.
7. The correct expression is [tex]\( n - 31 \)[/tex].
- This statement is true. This is the correct expression that represents "a number, [tex]\( n \)[/tex], decreased by thirty-one."
8. To evaluate the expression, subtract 31 from 29.
- This statement is true. Evaluating the expression [tex]\( n - 31 \)[/tex] with [tex]\( n = 29 \)[/tex] involves subtracting 31 from 29, which results in -2.
### Conclusion
Based on the given analysis, the true statements are:
- This is a subtraction expression.
- To evaluate, substitute 29 for the variable in the expression.
- The correct expression is [tex]\( n - 31 \)[/tex].
- To evaluate the expression, subtract 31 from 29.
