# Question: how would we make x the subject of the equation - x= mc/2

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### 1 Answer

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'.

**Answer:**

**making x the 'subject' the equation is written as**

**x = -mc/2**