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

Answer 1

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

A. \(-10x + 4 = -10x + 4\)

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. \(-10x + 4 = 10x + 3\)

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

C. \(10x + 3 = -10x + 3\)

Rearranging gives:
\[
10x + 10x = 3 - 3 \implies 20x = 0 \implies x = 0
\]
This equation also has a single solution.

D. \(10x + 4 = 10x - 4\)

Rearranging gives:
\[
10x - 10x = -4 - 4 \implies 0 = -8
\]
This is a contradiction and thus has no solutions.

In summary, the equation that has infinite solutions is:

**A. \(-10x + 4 = -10x + 4\)**.