How many solutions does this equation have?

Question

4(x - 1/2) = 4x - 2

 

 

 

Answer 1

To find this out, we start solving the equation.

 

4(x - 1/2) = 4x - 2

 

First, you distribute:

 

4x - 2 = 4x - 2

 

At this point we notice that both sides are exactly identical.  This means that any value of x can be used since 4 times that number minus 2 will always equal 4 times that number minus 2.

 

We say that the equation has infinitely many solutions since any number can work.

Answer 2

4(x - 1/2) = 4x - 2

 

4x - 2 = 4x - 2                (distribute)

  4x = 4x                       (add 2 to both sides)

   x = x                            (divide both sides by 4)

 

A "solution" is any value of x that makes the equation true.  This equation is true for an infinite number of values of x.