Let's solve the equation step by step.
The given equation is:
\[ 5(2x + 2) - 4 = 2x + 6 \]
- Distribute the \( 5 \) on the left-hand side:
\[ 10x + 10 - 4 = 2x + 6 \]
- Simplify the left-hand side:
\[ 10x + 6 = 2x + 6 \]
- Now, subtract \( 2x \) from both sides:
\[ 10x - 2x + 6 = 6 \]
This simplifies to:
\[ 8x + 6 = 6 \]
- Next, subtract \( 6 \) from both sides:
\[ 8x = 0 \]
- Finally, divide both sides by \( 8 \):
\[ x = 0 \]
Now that we have solved for \( x \), let’s analyze the solution:
The equation simplifies to \( x = 0 \), which means there is exactly one solution.
The correct response is:
The equation has one solution: x = 0.