Question

Question

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

The equation has no solution.
The equation has no solution.

The equation has one solution: x=0
.
The equation has one solution: x equals 0 .

The equation has infinite solutions.
The equation has infinite solutions.

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 of the equation:

1. Distribute $5$ on the left side: $$5(2x)+5(2)-4=10x+10-4=10x+6$$

2. Now we 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 both sides by $8$: $$x=0$$

Since we found a single solution $x=0$, we conclude that the equation has one solution: $x=0$.

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