Solve the equation. Show your work and check your solution.
2(3x-5) + x + 4 = x + 6(x-1)
First, distribute the 2 and 6 on their respective terms:
6x - 10 + x + 4 = x + 6x - 6
Next, combine like terms:
7x - 6 = 7x - 6
We can see that both sides of the equation are equal, so there are infinitely many solutions. We can check this by plugging in any value of x and seeing that the equation is true. For example, if we let x = 3:
2(3(3)-5) + 3 + 4 = 3 + 6(3-1)
2(4) + 7 = 3 + 6(2)
8 + 7 = 15
Both sides are equal, so x = 3 is a solution. However, any value of x will work, so there are infinitely many solutions to this equation.