Which of the following equations have exactly one solution?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
-78x+52=-52x-78−78x+52=−52x−78minus, 78, x, plus, 52, equals, minus, 52, x, minus, 78
(Choice B)
B
58x+52=78x-7858x+52=78x−7858, x, plus, 52, equals, 78, x, minus, 78
(Choice C)
C
58x+52=-78x-7858x+52=−78x−7858, x, plus, 52, equals, minus, 78, x, minus, 78
(Choice D)
D
52x+52=52x-7852x+52=52x−78
To determine which of the equations have exactly one solution, we need to simplify each equation and look for any similarities or differences.
(Choice A)
-78x + 52 = -52x - 78
Simplifying, we can combine like terms:
-78x + 52x = -78 - 52
-26x = -130
Dividing both sides by -26, we get:
x = 5
This equation has exactly one solution.
(Choice B)
58x + 52 = 78x - 78
Simplifying, we can combine like terms:
-20x = -130
Dividing both sides by -20, we get:
x = 6.5
This equation also has exactly one solution.
(Choice C)
58x + 52 = -78x - 78
Simplifying, we can combine like terms:
136x = -130
Dividing both sides by 136, we get:
x = -0.956
This equation does not have exactly one solution.
(Choice D)
52x + 52 = 52x - 78
Simplifying, we can combine like terms:
52x = -130
Dividing both sides by 52, we get:
x = -2.5
This equation also has exactly one solution.
Therefore, the equations in Choices A, B, and D have exactly one solution.
To determine which of the equations have exactly one solution, we can compare the coefficients of the variable "x" in each equation.
Let's break down each equation:
(Choice A) -78x + 52 = -52x - 78
In this equation, the coefficient of "x" on the left side is -78, and on the right side is -52.
Since the coefficients are different, this equation does not have exactly one solution.
(Choice B) 58x + 52 = 78x - 78
Here, the coefficient of "x" on the left side is 58, and on the right side is 78.
Again, the coefficients are different, so this equation does not have exactly one solution.
(Choice C) 58x + 52 = -78x - 78
For this equation, the coefficient of "x" on the left side is 58, while on the right side it is -78.
Once more, the coefficients are different, so this equation does not have exactly one solution.
(Choice D) 52x + 52 = 52x - 78
In this equation, the coefficient of "x" on both sides is 52.
Since the coefficients are the same, this equation actually has an infinite number of solutions.
By subtracting 52x from both sides and simplifying, we get 52 = -78, which is not possible.
Thus, this equation is what we call an "identity" and has endless solutions.
In summary:
- Both choices A, B, and C do not have exactly one solution because the coefficients of "x" are different on both sides of the equations.
- Only choice D has an infinite number of solutions due to the coefficients being the same on both sides, resulting in an "identity" equation.
your post is gibberish. words stuck into the math, math repeated ad nauseum.
A appears to be
-78x+52=-52x-78
which is equivalent to
-78x + 52x = -78 - 52
-26x = -130
so there is a solution.
If you simplify each choice and wind up with something which is true for all x, such as 24 = 24 then there are infinitely many choices
if you wind up with something that is clearly false, such as 24 = -10 then there is no solution.
So, if you still need help, just type your equations so they make sense (ONE TIME ONLY) and then maybe we can get somewhere.
Remember: It's not my job to figure out what you mean.
It's your job to say it so clearly you cannot be misunderstood.
you have failed dismally in that regard.