Which of the following equations has a solution of-1/2?
× +1= 1/2
×-1/2=1
×-1=-1/2
×+1/2=-1
The equation ×+1/2=-1 has a solution of -1/2.
To find the equation that has a solution of -1/2, we can solve each equation for x and check if the resulting value is -1/2. Let's go through each equation:
1) × +1 = 1/2
To solve for ×, we need to isolate it on one side of the equation. Subtracting 1 from both sides:
× = 1/2 - 1
Simplifying:
× = -1/2
The resulting value of × is -1/2, so this equation has a solution of -1/2.
2) × - 1/2 = 1
To solve for ×, we need to isolate it on one side of the equation. Adding 1/2 to both sides:
× = 1 + 1/2
Simplifying:
× = 3/2
The resulting value of × is not -1/2, so this equation does not have a solution of -1/2.
3) × - 1 = -1/2
To solve for ×, we need to isolate it on one side of the equation. Adding 1 to both sides:
× = -1/2 + 1
Simplifying:
× = 1/2
The resulting value of × is not -1/2, so this equation does not have a solution of -1/2.
4) × + 1/2 = -1
To solve for ×, we need to isolate it on one side of the equation. Subtracting 1/2 from both sides:
× = -1 - 1/2
Simplifying:
× = -3/2
The resulting value of × is not -1/2, so this equation does not have a solution of -1/2.
Therefore, the equation × + 1 = 1/2 has a solution of -1/2.
To determine which equation has a solution of -1/2, let's solve each equation by isolating the variable ×.
1) × + 1 = 1/2:
To isolate ×, we subtract 1 from both sides:
× = 1/2 - 1
× = 1/2 - 2/2
× = -1/2
2) × - 1/2 = 1:
To isolate ×, we add 1/2 to both sides:
× - 1/2 + 1/2 = 1 + 1/2
× = 3/2
3) × - 1 = -1/2:
To isolate ×, we add 1 to both sides:
× - 1 + 1 = -1/2 + 1
× = -1/2 + 2/2
× = 1/2
4) × + 1/2 = -1:
To isolate ×, we subtract 1/2 from both sides:
× + 1/2 - 1/2 = -1 - 1/2
× = -3/2
Therefore, the equation that has a solution of -1/2 is × + 1 = 1/2.