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 one solution: x=10.
The equation has one solution: x equals 10 .

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

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

The equation has no solutio

1 answer

To solve the equation \( 5(2x+2)−7x=3x+6 \), let's start by simplifying and then solving for \( x \).

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

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

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

The equation \( 10 = 6 \) is a contradiction and is never true.

Since we reached a contradiction, this equation has no solutions.

So, the answer is:

  • The equation has no solution.