Which of the following equations has the solution set {−3} ? Responses 4x−8=4 4 x minus 8 equals 4 4x+8=−4 4 x plus 8 equals negative 4 4x+8=4 4 x plus 8 equals 4 4x−8=−4
The equation that has the solution set {-3} is 4x+8=−4.
To determine which equation has the solution set {-3}, we need to substitute -3 for x in each equation and check if it satisfies the equation.
1. 4x - 8 = 4
Substituting -3 for x:
4(-3) - 8 = 4
-12 - 8 = 4
-20 = 4
Since -20 is not equal to 4, this equation does not have the solution set {-3}.
2. 4x + 8 = -4
Substituting -3 for x:
4(-3) + 8 = -4
-12 + 8 = -4
-4 = -4
Since -4 is equal to -4, this equation has the solution set {-3}.
3. 4x + 8 = 4
Substituting -3 for x:
4(-3) + 8 = 4
-12 + 8 = 4
-4 = 4
Since -4 is not equal to 4, this equation does not have the solution set {-3}.
4. 4x - 8 = -4
Substituting -3 for x:
4(-3) - 8 = -4
-12 - 8 = -4
-20 = -4
Since -20 is not equal to -4, this equation does not have the solution set {-3}.
Therefore, the equation that has the solution set {-3} is 4x + 8 = -4.
To determine which equation has the solution set {-3}, we can substitute -3 for x in each equation and see which equation gives us a true statement.
1) 4x - 8 = 4:
Substituting x = -3, we get: 4(-3) - 8 = 4
Simplifying: -12 - 8 = 4
-20 = 4, which is false.
2) 4x + 8 = -4:
Substituting x = -3, we get: 4(-3) + 8 = -4
Simplifying: -12 + 8 = -4
-4 = -4, which is true.
3) 4x + 8 = 4:
Substituting x = -3, we get: 4(-3) + 8 = 4
Simplifying: -12 + 8 = 4
-4 = 4, which is false.
4) 4x - 8 = -4:
Substituting x = -3, we get: 4(-3) - 8 = -4
Simplifying: -12 - 8 = -4
-20 = -4, which is false.
Among these equations, only the equation 4x + 8 = -4 gives a true statement when x = -3. Therefore, the equation 4x + 8 = -4 has the solution set {-3}.