Answer: Let's solve each equation step by step to determine the number of solutions:
3/2(2x+6)=3x+9
First, we distribute the 3/2 on the left side:
3x + 9 = 3x + 9
Subtracting 3x from both sides, we get:
9 = 9
This means that the equation is an identity and is true for all values of x. Therefore, it has infinitely many solutions.
3x+5=3(x+5)
Expanding the right side:
3x + 5 = 3x + 15
Subtracting 3x from both sides, we get:
5 = 15
This is a contradiction, so the equation has no solution.
x+4x+4=3(2x-1)
Simplifying the left side:
5x + 4 = 6x - 3
Adding 3 to both sides and subtracting 5x from both sides, we get:
7 = x
Therefore, the equation has one solution, x = 7.
6x+4x+1=2(5x+1)
Simplifying both sides:
10x + 1 = 10x + 2
Subtracting 10x from both sides, we get:
1 = 2
This is a contradiction, so the equation has no solution.
Explanation: