Which of the following equations has a solution of −12 ?(1 point) Responses x − 12 = 1 x minus Start Fraction 1 over 2 End Fraction equals 1 x − 1 = −12 x minus 1 equals negative Start Fraction 1 over 2 End Fraction x + 12 = −1 x plus Start Fraction 1 over 2 End Fraction equals negative 1 x + 1 = 12
To determine which equation has a solution of −12, we can substitute −12 into each equation and see which one is true.
1. x − 12 = 1:
Substituting −12:
(−12) − 12 = 1,
−24 = 1,
This equation is not true.
2. x − 1/2 = 1:
Substituting −12:
(−12) − 1/2 = 1,
−12 1/2 ≠ 1,
This equation is not true.
3. x − 1 = −12:
Substituting −12:
(−12) − 1 = −12,
−13 = −12,
This equation is true.
4. x + 12 = −1:
Substituting −12:
(−12) + 12 = −1,
0 = −1,
This equation is not true.
5. x + 1 = 12:
Substituting −12:
(−12) + 1 = 12,
−11 = 12,
This equation is not true.
Therefore, the equation x − 1 = −12 has a solution of −12.
To determine which of the equations has a solution of -12, we need to plug in -12 into each equation and see if it results in a true statement. Let's check each equation one by one:
1) x - 12 = 1
If we substitute x = -12 into this equation, we get (-12) - 12 = 1, which simplifies to -24 = 1. This is not true, so -12 is not a solution to this equation.
2) x - 1/2 = 1
If we substitute x = -12 into this equation, we get (-12) - 1/2 = 1, which simplifies to -12.5 = 1. This is not true, so -12 is not a solution to this equation.
3) x - 1 = -12
If we substitute x = -12 into this equation, we get (-12) - 1 = -12, which simplifies to -13 = -12. This is not true, so -12 is not a solution to this equation.
4) x + 12/2 = -1
If we substitute x = -12 into this equation, we get (-12) + 12/2 = -1, which simplifies to -6 + 6 = -1. This is true, so -12 is a solution to this equation.
5) x + 1 = 12
If we substitute x = -12 into this equation, we get (-12) + 1 = 12, which simplifies to -11 = 12. This is not true, so -12 is not a solution to this equation.
Therefore, the equation x + 12/2 = -1 has a solution of -12.
The equation that has a solution of −12 is:
x + 12 = -1