Which of the following equations has a solution of −1 over 2 ?
x − 1 over 2 = 1
x + 1 over 2 = −1
x + 1 = 1 over 2
x − 1 = −1 over 2
The equation that has a solution of -1/2 is:
x + 1 over 2 = -1
To find which equation has a solution of -1/2, we can substitute -1/2 into each equation and see which one satisfies the equation.
Let's substitute -1/2 into each equation:
1) x - 1/2 = 1
Substituting -1/2 into x, we get: -1/2 - 1/2 = 1
This simplifies to: -1 = 1
Since -1 is not equal to 1, this equation does not have a solution of -1/2.
2) x + 1/2 = -1
Substituting -1/2 into x, we get: -1/2 + 1/2 = -1
This simplifies to: 0 = -1
Since 0 is not equal to -1, this equation does not have a solution of -1/2.
3) x + 1 = 1/2
Substituting -1/2 into x, we get: -1/2 + 1 = 1/2
This simplifies to: 1/2 = 1/2
Since 1/2 is equal to 1/2, this equation has a solution of -1/2.
4) x - 1 = -1/2
Substituting -1/2 into x, we get: -1/2 - 1 = -1/2
This simplifies to: -3/2 = -1/2
Since -3/2 is equal to -1/2, this equation has a solution of -1/2.
Therefore, the equations that have a solution of -1/2 are:
x + 1 = 1/2
x - 1 = -1/2
To determine which equation has a solution of -1/2, we can solve each equation and see if -1/2 is a valid solution.
Let's solve each equation step by step:
1. x - 1/2 = 1:
To solve this equation, we can isolate x by adding 1/2 to both sides:
x - 1/2 + 1/2 = 1 + 1/2
x = 3/2
The solution to this equation is x = 3/2, not -1/2.
2. x + 1/2 = -1:
To solve this equation, we can isolate x by subtracting 1/2 from both sides:
x + 1/2 - 1/2 = -1 - 1/2
x = -3/2
The solution to this equation is x = -3/2, which is indeed -1/2.
3. x + 1 = 1/2:
To solve this equation, we can isolate x by subtracting 1 from both sides:
x + 1 - 1 = 1/2 - 1
x = -1/2
The solution to this equation is x = -1/2, which matches the given solution.
4. x - 1 = -1/2:
To solve this equation, we can isolate x by adding 1 to both sides:
x - 1 + 1 = -1/2 + 1
x = 1/2
The solution to this equation is x = 1/2, not -1/2.
Therefore, the equation that has a solution of -1/2 is x + 1/2 = -1.