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

Question

5(2x+2)-7x=3x+6

A. the equation has no solution
B. the equation has one solution: x = 10
C. the equation has one solution: x = 6
D. the equation has infinite solutions

Answer 1

To solve the equation 5(2x + 2) - 7x = 3x + 6, first distribute 5 to 2x and 2, which gives 10x + 10 - 7x = 3x + 6.

Next, combine like terms: 10x - 7x + 10 = 3x + 6

Combine further: 3x + 10 = 3x + 6

Subtract 3x from both sides of the equation: 10 = 6

This is not a true equation since 10 is not equal to 6.

Therefore, the equation has no solution.

The correct answer is A. the equation has no solution.