Question

Which of the following equations have exactly one solution?

Answer 1

Answer

a

Step-by-step explanation:

it must =180

Answer 2

The equations which have exactly one solution are:

Choice A: $-78x+52=-52x-78$

Choice C: $58x+52=78x-78$

Choice D: $58x+52=-78x-78$

Explanation:

Choice A: $-78x+52=-52x-78$

Adding both sides by 52x, we have,

$-26x+52=-78$

Subtracting both sides by 52,

$-26x=-130$

Dividing both sides by -26,

$x=5$

Hence, the equation $-78x+52=-52x-78$ has exactly one solution.

Thus, Choice A is the correct answer.

Choice B: $52 x+52=52 x-78$

Subtracting both sides by 52x,

$52=-78$

Since, both sides are not equal.

It has no solution.

Thus, Option B is not the correct answer.

Choice C: $58x+52=78x-78$

Subtracting both sides by 78x,

$-20x+52=-78$

Subtracting both sides by 52,

$-20 x=-130$

Dividing both sides by -20,

$x=6.5$

Hence, the equation $58x+52=78x-78$ has exactly one solution.

Thus, Choice C is the correct answer.

Option D: $58x+52=-78x-78$

Adding both sides by 78x,

$136x+52=-78$

Subtracting both sides by 52,

$136x=-130$

Dividing both sides by 136,

$x=-\frac{65}{68}\\x=-0.956$

Hence, the equation $58x+52=-78x-78$ has exactly one solution.

Thus, Choice D is the correct answer.