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 infinite solutions. The equation has infinite solutions. The equation has one solution: x=0 . The equation has one solution: x equals 0 . The equation has one solution: x=1 . The equation has one solution: x equals 1 . The equation has no solution.

1 answer

Let's solve the equation \( 5(2x+2) - 4 = 2x + 6 \).

First, simplify the left side:

\[ 5(2x + 2) - 4 = 10x + 10 - 4 = 10x + 6 \]

So now the equation is:

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

Next, we can 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 by 8:

\[ x = 0 \]

Lastly, let's check if there are infinite solutions or one solution. We can see that \( 10x + 6 = 2x + 6 \) is true for only the particular value of \( x = 0 \), and both sides of the equation reduce to \( 6 \).

Thus, the equation has one solution: \( x = 0 \).

The correct responses are:

  • The equation has one solution: \( x = 0 \).