Which of the following equations has a solution of -1/2?
x + 1/2 = -1
x - 1/2 = 1
x + 1 = 1/2
x - 1 = -1/2
The equation that has a solution of -1/2 is x - 1 = -1/2.
To find the equation that has a solution of -1/2, we need to solve each equation and see which one evaluates to -1/2. Let's go through each equation:
1. x + 1/2 = -1
Subtracting 1/2 from both sides, we get:
x = -1 - 1/2
Simplifying:
x = -3/2
2. x - 1/2 = 1
Adding 1/2 to both sides, we get:
x = 1 + 1/2
Simplifying:
x = 3/2
3. x + 1 = 1/2
Subtracting 1 from both sides, we get:
x = 1/2 - 1
Simplifying:
x = -1/2
4. x - 1 = -1/2
Adding 1 to both sides, we get:
x = -1/2 + 1
Simplifying:
x = 1/2
From the calculations, we can see that the equation x = -1/2 is the one that has a solution of -1/2.
To determine which equation has a solution of -1/2, we need to solve each equation and check if the value of x is -1/2.
Let's solve each equation one by one:
1. x + 1/2 = -1
To isolate x, we subtract 1/2 from both sides:
x = -1 - 1/2
x = -2/2 - 1/2
x = -3/2
Since -3/2 is not equal to -1/2, this equation does not have a solution of -1/2.
2. x - 1/2 = 1
To isolate x, we add 1/2 to both sides:
x = 1 + 1/2
x = 2/2 + 1/2
x = 3/2
Since 3/2 is not equal to -1/2, this equation does not have a solution of -1/2.
3. x + 1 = 1/2
To isolate x, we subtract 1 from both sides:
x = 1/2 - 1
x = 1/2 - 2/2
x = -1/2
This equation has a solution of x = -1/2.
4. x - 1 = -1/2
To isolate x, we add 1 to both sides:
x = -1/2 + 1
x = -1/2 + 2/2
x = 1/2
Since 1/2 is not equal to -1/2, this equation does not have a solution of -1/2.
Therefore, the equation x + 1 = 1/2 is the only equation that has a solution of -1/2.