Which of the following equations has a solution of −12 ?(1 point)
Responses
x + 12 = −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 − 12 = 1
x minus Start Fraction 1 over 2 End Fraction equals 1
x + 1 = 12
The equation that has a solution of -12 is x + 12 = −1.
To determine which equation has a solution of -12, we need to substitute -12 for the variable x in each equation and see which one results in a true statement.
Let's check each equation:
1. x + 12 = -1
Substituting -12 for x, we get:
-12 + 12 = -1
0 = -1 (false statement)
2. x + 1/2 = -1
Substituting -12 for x, we get:
-12 + 1/2 = -1
-11.5 ≠ -1 (false statement)
3. x - 1 = -12
Substituting -12 for x, we get:
-12 - 1 = -12
-13 = -12 (false statement)
4. x + 1 = 12
Substituting -12 for x, we get:
-12 + 1 = 12
-11 = 12 (false statement)
From the calculations, none of the equations have a solution of -12.
To find the equation that has a solution of -12, we need to substitute -12 for 'x' and see which equation is true.
Let's go through each option:
Option 1: x + 12 = -1
Substituting -12 for 'x': -12 + 12 = -1
Simplifying: 0 = -1
This equation is not true, so it does not have a solution of -12.
Option 2: x + 1/2 = -1
Substituting -12 for 'x': -12 + 1/2 = -1
Simplifying: -23/2 = -1
This equation is not true, so it does not have a solution of -12.
Option 3: x - 1 = -12
Substituting -12 for 'x': -12 - 1 = -12
Simplifying: -13 = -12
This equation is true, so it has a solution of -12.
Option 4: x + 1 = 12
Substituting -12 for 'x': -12 + 1 = 12
Simplifying: -11 = 12
This equation is not true, so it does not have a solution of -12.
Therefore, the equation that has a solution of -12 is x - 1 = -12.