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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
.

1 answer

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: \(x = 0\).