Let's solve the equation step by step:
The equation is:
\[ 5(2x + 2) - 4 = 2x + 6 \]
First, we will distribute the \(5\) on the left side:
\[ 10x + 10 - 4 = 2x + 6 \]
Now simplify the left side:
\[ 10x + 6 = 2x + 6 \]
Next, we will get all terms involving \(x\) on one side and constant terms on the other side. Subtract \(2x\) from both sides:
\[ 10x - 2x + 6 = 6 \]
This simplifies to:
\[ 8x + 6 = 6 \]
Now, subtract \(6\) from both sides:
\[ 8x = 0 \]
Now, divide both sides by \(8\):
\[ x = 0 \]
Now let's determine the solution:
- We found one solution: \(x = 0\).
Next, we need to check if there are infinite solutions or no solutions. This can be done by checking if the two sides of the equation are equivalent when all variables are eliminated.
After isolating the variable, we didn't end up with a contradiction (like \(0 = 1\)), which indicates that there are not no solutions.
Thus, the original equation has one solution: x = 0.
So the correct response is:
The equation has one solution: x equals 0.