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

Nov 23, 2016

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..

$2 \left(3 x - 4\right) = - \left(8 - 6 x\right)$

$6 x - 8 = - 8 + 6 x \text{ } L H S = R H S$

$6 x - 6 x = - 8 + 8$

$0 = 0$

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.