Which of the following equations has a solution of −1/2 ?(1 point)
Responses
x − 1/2 = 1
x minus Start Fraction 1 over 2 End Fraction equals 1
x + 1/2 = −1
x plus Start Fraction 1 over 2 End Fraction equals negative 1
x + 1 = 1/2
x plus 1 equals Start Fraction 1 over 2 End Fraction
x − 1 = −1/2
x minus 1 equals negative Start Fraction 1 over 2 End Fraction
The equation x − 1/2 = 1 has a solution of −1/2.
To determine which equation has a solution of -1/2, we need to substitute -1/2 into each equation and see which equation is true.
Let's substitute -1/2 into each equation:
1) x - 1/2 = 1
Substituting -1/2 for x gives: -1/2 - 1/2 = 1
This simplifies to: -1 = 1
This equation is not true.
2) x + 1/2 = -1
Substituting -1/2 for x gives: -1/2 + 1/2 = -1
This simplifies to: 0 = -1
This equation is not true.
3) x + 1 = 1/2
Substituting -1/2 for x gives: -1/2 + 1 = 1/2
This simplifies to: 1/2 = 1/2
This equation is true.
4) x - 1 = -1/2
Substituting -1/2 for x gives: -1/2 - 1 = -1/2
This simplifies to: -3/2 = -1/2
This equation is not true.
Therefore, the equation x + 1 = 1/2 has a solution of -1/2.
To find out which of the given equations has a solution of -1/2, we can solve each equation by isolating the variable (x) and then substitute -1/2 into the equation to check if it satisfies the equation.
Let's go through each equation to find the solution:
1) x - 1/2 = 1
To solve this equation, we can add 1/2 to both sides:
x - 1/2 + 1/2 = 1 + 1/2
x = 3/2
Substituting -1/2 into this equation yields:
-1/2 = 3/2
Since -1/2 is not equal to 3/2, this equation does not have a solution of -1/2.
2) x + 1/2 = -1
To solve this equation, we can subtract 1/2 from both sides:
x + 1/2 - 1/2 = -1 - 1/2
x = -3/2
Substituting -1/2 into this equation yields:
-1/2 = -3/2
Since -1/2 is equal to -3/2, this equation has a solution of -1/2.
3) x + 1 = 1/2
To solve this equation, we can subtract 1 from both sides:
x + 1 - 1 = 1/2 - 1
x = -1/2
Substituting -1/2 into this equation yields:
-1/2 = -1/2
Since -1/2 is equal to -1/2, this equation has a solution of -1/2.
4) x - 1 = -1/2
To solve this equation, we can add 1 to both sides:
x - 1 + 1 = -1/2 + 1
x = 1/2
Substituting -1/2 into this equation yields:
-1/2 = 1/2
Since -1/2 is not equal to 1/2, this equation does not have a solution of -1/2.
Therefore, the equations that have a solution of -1/2 are:
x + 1/2 = -1
x + 1 = 1/2