Question

Which equation has infinitely many solutions?
Responses
A


= 4x + 54 x + 3 3 = 4x + 5
B


= 5x + 410 x + 8 2 = 5x + 4
C


= 2x − 28 x − 5 3 = 2x − 2
D


= 4x − 68 x − 5 2 = 4x − 6

Answer 1

To determine which equation has infinitely many solutions, we need to explore each option to see if any of them can be simplified to a true statement that holds for any value of \(x\).

**Option A:**
\[
4x + 54 = 4x + 5
\]
Subtracting \(4x\) from both sides:
\[
54 = 5
\]
This is a false statement, hence there are no solutions.

---

**Option B:**
\[
10x + 8 = 5x + 4
\]
Subtracting \(5x\) from both sides:
\[
5x + 8 = 4
\]
Subtracting 8 from both sides:
\[
5x = -4
\]
Dividing by 5:
\[
x = -\frac{4}{5}
\]
This equation has one solution.

---

**Option C:**
\[
28x - 5 = 2x - 2
\]
Subtracting \(2x\) from both sides:
\[
26x - 5 = -2
\]
Adding 5 to both sides:
\[
26x = 3
\]
Dividing by 26:
\[
x = \frac{3}{26}
\]
This equation has one solution.

---

**Option D:**
\[
2x - 5 = 4x - 6
\]
Subtracting \(2x\) from both sides:
\[
-5 = 2x - 6
\]
Adding 6 to both sides:
\[
1 = 2x
\]
Dividing by 2:
\[
x = \frac{1}{2}
\]
This equation has one solution.

---

Since none of the equations resulted in a true statement that holds for all \(x\), but all provided only one solution, we conclude that none of the options have infinitely many solutions.

If you meant to include more specific context or if there are variations of the equations, please provide them for a more accurate evaluation.