Question

Solve for the indicated variable. -10=xy + z for x

Answer 1

To solve for x, you undo what was done to x. The variable x is ...

• multiplied by y
• added to z

You "undo" these operations in the reverse order, so first we undo the addition of z. We accomplish that by adding the opposite of z:

... -10 -z = xy

Now, we undo the multiplication by y. We accomplish that by multipying by the reciprocal of y.

... (-10 -z)/y = x

We can rearrange this, if you like.

$x=\dfrac{-10-z}{y}$

And, if you want, you can factor out the minus sign.

$x=-\left(\dfrac{z+10}{y}\right)$