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

The equation has infinite solutions.

The equation has no solution.

The equation has one solution: x=0 .

The equation has one solution: x=1 .

1 answer

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:

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

  1. Combine like terms on the left side:

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

  1. Now, isolate the \( x \) terms by subtracting \( 2x \) from both sides:

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

This simplifies to:

\[ 8x + 6 = 6 \]

  1. Subtract \( 6 \) from both sides:

\[ 8x = 0 \]

  1. 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: \( x = 0 \).