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Solve for a to determine if the equation has one, none, or infinite solutions.

5(2x + 2) - 4 = 2x + 6 (1 point)

The equation has one solution: x = 1

The equation has infinite solutions.

The equation has one solution: x = 0

The equation has no solution.

1 answer

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

  1. Distributive property: \[ 5(2x + 2) = 10x + 10 \]

    Substitute this back into the equation: \[ 10x + 10 - 4 = 2x + 6 \]

  2. Simplify the left side: \[ 10x + 6 = 2x + 6 \]

  3. Now, we can isolate \(x\) by subtracting \(2x\) from both sides: \[ 10x - 2x + 6 = 6 \] \[ 8x + 6 = 6 \]

  4. Next, subtract 6 from both sides: \[ 8x = 0 \]

  5. Finally, divide by 8: \[ x = 0 \]

Now, we need to check how many solutions this equation has:

  • We have found \(x = 0\), and the steps followed show a consistent relationship demonstrated in the equation.

This tells us that the equation has one solution: \(x = 0\).

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