what's the value of a-b?

Question

1/2(6x-4)-(3-x)=ax+x+b

 

If the equation above has infinitely many solutions, what's the value of a-b?

Answer 1

For this to have infinitely many solutions, the left and right sides of the equation must be the same

 

1/2 (6x - 4) - (3 - x) = ax + x + b

 

3x - 2 - 3 + x = (a + 1)x + b

 

4x - 5 = (a + 1)x + b

 

Set a + 1 = 4

 

a = 4 - 1 = 3

 

In order for the right hand side to be the same as the left, then a must equal 3, and b must equal -5. 

Answer 2

left side of the given identity can be simplified to 3x-2-3+x=4x-5=3x+x-5

so we have 3x+x-5=ax+x+b. if the algebraic function on either side of the equation are same, there are going to be infinite solutions. (isn't it??) so, here, that happens when a=3 and b=-5. then a-b=3-(-5)=3+5=8