Which of the following equations have exactly one solution?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
52x+52=52x-7852x+52=52x−7852, x, plus, 52, equals, 52, x, minus, 78
(Choice B)
B
-78x+52=-52x-78−78x+52=−52x−78minus, 78, x, plus, 52, equals, minus, 52, 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
58x+52=78x-7858x+52=78x−78
To determine which equations have exactly one solution, we need to compare the coefficients of x on both sides of each equation.
Let's go through each choice:
Choice A: 52x + 52 = 52x - 78
This equation has the same coefficient of x on both sides of the equation (52). Therefore, it is always true and has infinitely many solutions, not exactly one.
Choice B: -78x + 52 = -52x - 78
This equation has different coefficients of x on both sides of the equation (-78 and -52). Therefore, it will have exactly one solution since the coefficients are not equal.
Choice C: 58x + 52 = -78x - 78
This equation has different coefficients of x on both sides of the equation (58 and -78). Therefore, it will have exactly one solution since the coefficients are not equal.
Choice D: 58x + 52 = 78x - 78
This equation has different coefficients of x on both sides of the equation (58 and 78). Therefore, it will have exactly one solution since the coefficients are not equal.
From the given choices, the equations that have exactly one solution are:
- Choice B: -78x + 52 = -52x - 78
- Choice C: 58x + 52 = -78x - 78
- Choice D: 58x + 52 = 78x - 78
To determine which equations have exactly one solution, we need to simplify each equation and compare the coefficients of the variable that represents x.
Let's simplify each equation step by step:
(Choice A)
52x + 52 = 52x - 78
Subtract 52x from both sides:
52 = -78
This is not possible, so there is no solution.
(Choice B)
-78x + 52 = -52x - 78
Add 78x to both sides:
52 = 26x - 78
Add 78 to both sides:
130 = 26x
Divide both sides by 26:
5 = x
This equation has exactly one solution, which is x = 5.
(Choice C)
58x + 52 = -78x - 78
Add 78x to both sides:
58x + 78x + 52 = -78
Combine like terms:
136x + 52 = -78
This equation does not simplify to a single-variable form, as x does not have a coefficient on one side. Therefore, there is no solution.
(Choice D)
58x + 52 = 78x - 78
Subtract 58x from both sides:
52 = 20x - 78
Add 78 to both sides:
130 = 20x
Divide both sides by 20:
6.5 = x
This equation has exactly one solution, which is x = 6.5.
So, the equations that have exactly one solution are Choice B: -78x + 52 = -52x - 78, and Choice D: 58x + 52 = 78x - 78.
why do you duplicate everything? And then do it again in words!? Very annoying!
First step, simplify the equation. For example,
52x+52=52x-78
52 = -78
Nope, no solutions there
Do the others. If your equation reduces to something that is false, there are no solutions. If it turns out always true, then there are infinitely many solutions.
Come back if you get stuck.