Question

Which equation has infinitely many solutions?
A
−8x+3=8x−8x+3=8x
B
0=8x−8x0=8x−8x
C
8x−3x=158x−3x=15
D
8x=1+8x8x=1+8x

Answer 1

To determine which equation has infinitely many solutions, we need to analyze each option:

**A:**

\[
-8x + 3 = 8x
\]

Rearranging gives:

\[
3 = 8x + 8x
\]
\[
3 = 16x \implies x = \frac{3}{16}
\]

This equation has a single solution \( x = \frac{3}{16} \).

---

**B:**

\[
0 = 8x - 8x
\]

Simplifying gives:

\[
0 = 0
\]

This is true for all values of \( x \). Therefore, this equation has infinitely many solutions.

---

**C:**

\[
8x - 3x = 15
\]

Simplifying gives:

\[
5x = 15 \implies x = 3
\]

This equation has a single solution \( x = 3 \).

---

**D:**

\[
8x = 1 + 8x
\]

Subtracting \( 8x \) from both sides gives:

\[
0 = 1
\]

This is a false statement, so this equation has no solutions.

---

Based on the analysis, the equation that has infinitely many solutions is:

**B: \( 0 = 8x - 8x \)**.