Solve for x

Question

–9x+12+4(3x-3)= 7(x-2)-4x+14

 

-9x+12+12x-12=7x-14-4x+14

-9x+12x=7x-4x

3x=3x

x=x

 

Is this correct?  And does  it mean infinite solutions?

Answer 1

Your work is correct and the fact that you get x = x means that the equation on each side of the equal sign represents the same line thus, there are an infinite variety of answers.

Answer 2

Your work looks correct, when you reach x=x this means the equation is true for any x value.  You can test this out by choosing a random number for x, see what you get plugging it into the left side (–9x+12+4(3x-3)), and the plug that same x into the right side (7(x-2)-4x+14) you should get the same value.