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 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 . The equation has one solution: x equals 1 . The equation has no solution.

Answer 1

To solve the equation \( 5(2x + 2) - 4 = 2x + 6 \), let's start by simplifying both sides.

1. Distribute the 5 on the left side:

\[ 5(2x) + 5(2) - 4 = 2x + 6 \]

\[ 10x + 10 - 4 = 2x + 6 \]

2. Simplifying the left side gives us:

\[ 10x + 6 = 2x + 6 \]

3. Now, we will get all \( x \) terms on one side and constant terms on the other side:

\[ 10x - 2x = 6 - 6 \]

\[ 8x = 0 \]

4. Dividing both sides by 8, we get:

\[ x = 0 \]

Now, let's analyze the solution:

• We found one solution, which is \( x = 0 \).

The equation has one solution: \( x = 0 \). Therefore, the correct answers are:

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

Both responses are valid.