Which of the following equations has the given solution set?
Solution set: Ø
A)-2m + 5 = 2m + 5
B)-2m + 5 = -2m + 5
C)-2m + 5 = -2m - 5
D)none
The solution set of Ø means that there is no solution to the equation. This happens when the equation is inconsistent.
For example, the equation
5x-5x+3=0
is inconsistent because 5x-5x=0, so the equation implies 3=0, which is impossible. So the solution set is Ø.
See if you could identify a similar case in equations A, B or C. If you obtain a solution in all three equations, then the answer is D (none).
To determine which equation has the given solution set of "Ø" (also known as an empty set or no solution), we need to examine the equations and see if there are any values of "m" that satisfy the equation.
Let's analyze each equation and solve for "m":
A) -2m + 5 = 2m + 5
To solve this equation, we can start by eliminating the constant terms (5) on both sides:
-2m = 2m
Next, we simplify the equation by combining like terms:
-2m - 2m = 0
-4m = 0
By dividing both sides by -4, we get:
m = 0
This solution does not satisfy the given equation since we end up with a contradiction (0 ≠ 2m).
B) -2m + 5 = -2m + 5
This equation simplifies to:
0 = 0
This equation is always true, regardless of the value of "m". However, since we are looking for a specific solution set (Ø), this equation is not the answer.
C) -2m + 5 = -2m - 5
By simplifying this equation, we have:
0 = -10
This equation is false, indicating that no value of "m" can satisfy it.
D) None of the given equations
Since none of the equations have a solution that satisfies the condition, "none" is the correct answer.
To summarize, the equation with the given solution set "Ø" is D) none.