Question

How do you solve for c in `a(b – c) = d`?

Answer 1

`c=b-d/a`

Explanation:

Given: `a(b-c)=d`

Divide by `a` on both sides.

`(color(red)cancelcolor(black)a(b-c))/(color(red)cancelcolor(black)a)=d/a`

`b-c=d/a`

Subtract `b` from both sides.

`color(red)cancelcolor(black)b-color(red)cancelcolor(black)b-c=d/a-b`

`-c=d/a-b`

Reverse signs.

`:.c=-(d/a-b)`

`=b-d/a`

Answer 2

`c=b-d/a`

Explanation:

`"divide both sides by a"`

`cancel(a)/cancel(a)(b-c)=d/a`

`rArrb-c=d/a`

`"subtract b from both sides"`

`cancel(b)-cancel(b)-c=d/a-b`

`rArr-c=d/a-b`

`"multiply all terms on both sides by "-1`

`rArrc=-d/a+b`

`rArrc=b-d/a`