Which of the following equations has infinite solutions?

Question

Which of the following equations has infinite solutions?
A. -10×+4= -10×+4
B. -10×+4=10×+3
C. 10x+3=-10×+3
D. 10x+4=10×-4

GPT-4o mini · Answer

To determine which of the equations has infinite solutions, we can analyze each one:

A. $- 10 x + 4 = - 10 x + 4$

This is an identity since both sides of the equation are exactly the same for any value of $x$ . Thus, it has infinite solutions.

B. $- 10 x + 4 = 10 x + 3$

Rearranging this gives: $- 10 x - 10 x = 3 - 4 ⟹ - 20 x = - 1 ⟹ x = \frac{1}{20}$ This equation has a single solution.

C. $10 x + 3 = - 10 x + 3$

Rearranging gives: $10 x + 10 x = 3 - 3 ⟹ 20 x = 0 ⟹ x = 0$ This equation also has a single solution.

D. $10 x + 4 = 10 x - 4$

Rearranging gives: $10 x - 10 x = - 4 - 4 ⟹ 0 = - 8$ This is a contradiction and thus has no solutions.

In summary, the equation that has infinite solutions is:

A. $- 10 x + 4 = - 10 x + 4$ .