Question

Solve for x to determine if the equation has one none or infinite solution.
5(2×+2)-4=2×+6

Answer 1

To solve the equation \( 5(2x+2)-4=2x+6 \), let's first simplify both sides.

1. Distribute the 5 on the left side:
\[
5(2x) + 5(2) - 4 = 10x + 10 - 4
\]
This simplifies to:
\[
10x + 6
\]

2. Now, rewrite the equation:
\[
10x + 6 = 2x + 6
\]

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

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

5. Finally, divide by 8:
\[
x = 0
\]

Now, let's check the solutions to determine whether the equation has one, none, or infinite solutions:

- Since we found one specific value for \( x \) (which is \( x = 0 \)), the equation has **one solution**.