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 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 no solution.
The equation has no solution.
The equation has one solution: x=10.
The equation has one solution: x equals 10 .
To solve for x, we can start by simplifying the equation:
5(2x+2) - 7x = 3x + 6
Distribute the 5:
10x + 10 - 7x = 3x + 6
Combine like terms on both sides:
3x + 10 = 3x + 6
Subtract 3x from both sides:
10 = 6
Since the equation simplifies to 10 = 6, which is not true, there are no solutions to the equation. Therefore, the correct response is:
The equation has no solution.
To solve for x, we will first simplify the equation:
5(2x+2) - 7x = 3x + 6
Start by distributing the 5 to the terms inside the parentheses:
10x + 10 - 7x = 3x + 6
Combine like terms on both sides of the equation:
10x - 7x + 10 = 3x + 6
3x + 10 = 3x + 6
We can see that the variable terms cancel out on both sides:
3x = 3x
This equation means that the variable term, 3x, is equal to itself, which is always true for any value of x. Therefore, the equation has infinite solutions.