Ask a New Question
Menu

Solve for x

to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6
(1 point)
Responses

The equation has no solution.
The equation has no solution.

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=6
.
The equation has one solution: x equals 6 .

The equation has one solution: x=10
.

1 answer

To solve the equation \( 5(2x + 2) - 7x = 3x + 6 \), we can start by simplifying the left-hand side.

  1. Distribute \( 5 \) in \( 5(2x + 2) \): \[ 5 \cdot 2x + 5 \cdot 2 = 10x + 10 \] So the equation becomes: \[ 10x + 10 - 7x = 3x + 6 \]

  2. Combine like terms on the left side: \[ (10x - 7x) + 10 = 3x + 6 \] Which simplifies to: \[ 3x + 10 = 3x + 6 \]

  3. Next, subtract \( 3x \) from both sides: \[ 10 = 6 \]

The equation \( 10 = 6 \) is a contradiction, meaning the equation has no solutions.

Thus, the correct response is: The equation has no solution.