Let's start by writing and solving the equation based on the given problem:
### Write and Solve the Equation
The problem states: "A number decreased by thirty-one is fifty-two." This can be translated mathematically as:
[tex]\[ n - 31 = 52 \][/tex]
To find the value of [tex]\( n \)[/tex], we need to isolate [tex]\( n \)[/tex] by adding 31 to both sides of the equation:
[tex]\[ n - 31 + 31 = 52 + 31 \][/tex]
[tex]\[ n = 83 \][/tex]
So, the solution to the equation is [tex]\( n = 83 \)[/tex].
### Checking the Solution
To verify our solution, we substitute [tex]\( 83 \)[/tex] back into the original equation [tex]\( n - 31 = 52 \)[/tex] and check if the equation holds true:
[tex]\[ 83 - 31 = 52 \][/tex]
[tex]\[ 52 = 52 \][/tex]
The calculated solution checks out, confirming that [tex]\( n = 83 \)[/tex] is correct.
### Identify True Statements
- The correct equation is [tex]\( n + 31 = 52 \)[/tex]: False.
- The correct equation based on the problem statement is [tex]\( n - 31 = 52 \)[/tex].
- The correct equation is [tex]\( n - 31 = 52 \)[/tex]: True.
- This reflects the problem statement accurately.
- To check the solution, substitute 83 for the variable in the equation: True.
- Substituting [tex]\( 83 \)[/tex] into the equation verifies it.
- To check the solution, substitute 21 for the variable in the equation: False.
- Substituting [tex]\( 21 \)[/tex] would not satisfy the equation, as [tex]\( 21 - 31 \neq 52 \)[/tex].
- This is an addition problem: False.
- This problem involves subtraction: a number decreased by 31.
- This is a subtraction problem: True.
- The keyword "decreased by" suggests a subtraction operation.
- To solve the equation, subtract 31 from both sides: False.
- We actually added 31 to both sides to isolate [tex]\( n \)[/tex].
- To solve the equation, add 31 to both sides: True.
- We added 31 to both sides of the equation to isolate and solve for [tex]\( n \)[/tex].
### In Summary
We have established the following as true statements:
- The correct equation is [tex]\( n - 31 = 52 \)[/tex].
- To check the solution, substitute 83 for the variable in the equation.
- This is a subtraction problem.
- To solve the equation, add 31 to both sides.
These are accurate representations based on the problem statement and the solution we derived.
