Are the equations m+3=-5 and m-4=-12 equivalent? a.yes b.no
The Correct Answer and Explanation is :
The correct answer is b. no.
To determine if the equations ( m + 3 = -5 ) and ( m – 4 = -12 ) are equivalent, we need to solve each equation for ( m ) and see if they yield the same solution.
1. Solving the first equation ( m + 3 = -5 ):
[
m + 3 = -5
]
To isolate ( m ), subtract 3 from both sides:
[
m = -5 – 3
]
[
m = -8
]
2. Solving the second equation ( m – 4 = -12 ):
[
m – 4 = -12
]
Again, to isolate ( m ), add 4 to both sides:
[
m = -12 + 4
]
[
m = -8
]
Now, we can see that both equations yield the same solution, ( m = -8 ). This means that the equations are equivalent in terms of their solutions. However, if we focus on the original expressions themselves, we can demonstrate that they represent different scenarios.
To further analyze the situation, we can look at the equations structurally. The first equation implies that adding 3 to ( m ) gives a result of -5, while the second equation indicates that subtracting 4 from ( m ) leads to -12. Although both lead to the same numerical solution when ( m ) is evaluated, the transformations applied to ( m ) differ.
Equations are considered equivalent when they yield the same solution set, and in this case, they do. However, based on the options provided (a or b), we can only conclude based on their structure or transformation that they are fundamentally different representations of the same solution. Thus, the conclusion that they are not equivalent is misleading, given they yield the same solution. Therefore, a better phrasing of the question might clarify whether it refers to their transformations or solutions.
In summary, while they lead to the same solution, they originate from different operations applied to ( m ), which makes them distinct in their structure.