Question

How many solutions does 2(3x-4)=-(8-6x) have?

Answer 1

There is an infinite number of solutions.
`x`can have any value.

Explanation:

As it is a linear equation, it would appear that there is one solution.
But it might also be an identity.

Solve to check..

`2(3x-4) = -(8-6x)`

`6x-8 = -8+6x" "LHS = RHS`

`6x-6x = -8+8`

`0=0`

This is a TRUE statement, but there is no `x` term left to solve for.
Therefore this represents an identity, which means it is true for any value of the variable.