To solve the equation \( 3(2x+2) - 4 = -2x + 10 \), let's start by simplifying both sides.
-
Distribute on the left side: \[ 3(2x) + 3(2) - 4 = 6x + 6 - 4 \] which simplifies to: \[ 6x + 2 \]
-
Now rewrite the equation: \[ 6x + 2 = -2x + 10 \]
-
Next, let's move all terms involving \( x \) to one side and constant terms to the other side. Start by adding \( 2x \) to both sides: \[ 6x + 2 + 2x = 10 \] This simplifies to: \[ 8x + 2 = 10 \]
-
Now, subtract \( 2 \) from both sides: \[ 8x = 8 \]
-
Finally, divide both sides by \( 8 \): \[ x = 1 \]
The solution is \( x = 1 \).
Now, we can check if this solution leads to one, none, or infinite solutions. Since we derived \( x = 1 \) and we arrived at a unique answer, this equation has one solution: \( x = 1 \).
So the correct response is:
The equation has one solution: x equals 1.