Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−4=2x+6 (1 point)

Question

The equation has infinite solutions.

The equation has no solution.

The equation has one solution: x=0 .

The equation has one solution: x=1 .

Answer 1

To solve the equation $5(2x+2)-4=2x+6$, we will first simplify both sides.

1. Distribute $5$ on the left side:

$$5(2x+2)=10x+10$$

So the equation becomes:

$$10x+10-4=2x+6$$

2. Combine like terms on the left side:

$$10x+6=2x+6$$

3. Now, isolate the $x$ terms by subtracting $2x$ from both sides:

$$10x-2x+6=6$$

This simplifies to:

$$8x+6=6$$

4. Subtract $6$ from both sides:

$$8x=0$$

5. Finally, divide by $8$:

$$x=0$$

Now, we determine how many solutions the equation has. We found a single solution, $x=0$.

Thus, the answer is: The equation has one solution: $x=0$.