Which of the following equations has a solution of −1/2 ?(1 point) Responses x + 1/2 = −1 x plus Start Fraction 1 over 2 End Fraction equals negative 1 x − 1 = −12 x minus 1 equals negative Start Fraction 1 over 2 End Fraction x + 1 = 1/2 x plus 1 equals Start Fraction 1 over 2 End Fraction x − 12 = 1 x minus Start Fraction 1 over 2 End Fraction equals 1
The equation that has a solution of −1/2 is x + 1/2 = −1
To find the equation with a solution of -1/2, we can substitute -1/2 into each equation and see if it satisfies the equation.
1) x + 1/2 = -1
Let's substitute -1/2 for x:
(-1/2) + 1/2 = -1
0 = -1
This equation is not satisfied, so it is not the correct answer.
2) x + (1/2) = -1
Let's substitute -1/2 for x:
(-1/2) + (1/2) = -1
0 = -1
This equation is also not satisfied, so it is not the correct answer.
3) x - 1 = -1/2
Let's substitute -1/2 for x:
(-1/2) - 1 = -1/2
-3/2 = -1/2
This equation is satisfied, so it is the correct answer.
4) x + 1 = 1/2
Let's substitute -1/2 for x:
(-1/2) + 1 = 1/2
1/2 = 1/2
This equation is also satisfied, but it does not have a solution of -1/2.
5) x - 1/2 = 1
Let's substitute -1/2 for x:
(-1/2) - 1/2 = 1
-1 = 1
This equation is not satisfied, so it is not the correct answer.
Therefore, the correct equation with a solution of -1/2 is x - 1 = -1/2.
To determine which equation has a solution of -1/2, we need to plug in -1/2 into each equation and see which one makes the equation true.
Let's test each equation with -1/2:
1) x + 1/2 = -1
When we substitute -1/2 for x, we get: (-1/2) + 1/2 = -1. Simplifying further, we have: 0 = -1, which is not true.
2) x - 1 = -1/2
When we substitute -1/2 for x, we get: (-1/2) - 1 = -1/2. Simplifying further, we have: -3/2 = -1/2, which is not true.
3) x + 1 = 1/2
When we substitute -1/2 for x, we get: (-1/2) + 1 = 1/2. Simplifying further, we have: 1/2 = 1/2, which is true.
4) x - 1/2 = 1
When we substitute -1/2 for x, we get: (-1/2) - 1/2 = 1. Simplifying further, we have: -1 = 1, which is not true.
Therefore, the equation that has a solution of -1/2 is x + 1 = 1/2.