When making a variable the 'subject' of an equation we isolate it on its own on the lefthand side of the equation.
If we are given the equation
` ``-x = mc``/2`
to make ` ``x` the subject we need to isolate it on its own on the lefthand side. This condition is nearly true in this case, except that `x` is multiplied by -1. Rewrite the equation as
`(-1) times x = m times c times` `1/2`
To isolate `x` on its own on the lefthand side divide both sides through by -1 giving
`x = m times c times 1/2 times 1/(-1)`
(Note: the -1 moves diagonally from the top left of the equation to the bottom right).
Using the fact that (-1) x (-1) = 1 we know then that 1/(-1) = -1. Rewriting the equation using this we have that
`x = m times c times 1/2 times (-1)`
Rewriting in the original shorthand (removing the multiplication signs) we have that
`x = - mc` `/2`
An alternative way would be to multiply both sides by -1 rather than divide. The -1 on the lefthand side at the beginning would be ` `'negated'.
making x the 'subject' the equation is written as
x = -mc/2