Question

5(2x+2)-4=2x+6 this equation has one none or infinite solution

Answer 1

To determine the number of solutions for the equation \( 5(2x + 2) - 4 = 2x + 6 \), let's simplify and solve it step by step.

1. **Distribute and simplify the left side:**
\[
5(2x + 2) = 10x + 10
\]
Therefore, the equation becomes:
\[
10x + 10 - 4 = 2x + 6
\]

2. **Combine like terms on the left side:**
\[
10x + 6 = 2x + 6
\]

3. **Subtract \(2x\) from both sides:**
\[
10x - 2x + 6 = 6
\]
This simplifies to:
\[
8x + 6 = 6
\]

4. **Next, subtract 6 from both sides:**
\[
8x = 0
\]

5. **Divide by 8:**
\[
x = 0
\]

Now we have found a single solution, \( x = 0 \).

To summarize:

- Since we have one solution \( x = 0 \), the equation has **exactly one solution**.