How do you solve for a in $ax+ z = aw-y$ ?

Question

18678 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-12T01:52:16

See a solution process below:

First, subtract $color(red)(z)$ and $color(blue)(aw)$ from each side of the equation to isolate the $a$ terms while keeping the equation balanced:

$ax - color(blue)(aw) + z - color(red)(z) = aw - color(blue)(aw) - y - color(red)(z)$

$ax - aw + 0 = 0 - y - z$

$ax - aw = -y - z$

Next, factor an $a$ from each term on the left side of the equation:

$a(x - w) = -y - z$

Now, divide each side of the equation by $color(red)(x - w)$ to solve for $a$ while keeping the equation balanced:

$(a(x - w))/color(red)(x - w) = (-y - z)/color(red)(x - w)$

$(acolor(red)(cancel(color(black)((x - w)))))/cancel(color(red)(x - w)) = (-y - z)/(x - w)$

$a = (-y - z)/(x - w)$

We can then multiply the right side of the equation by a form of $1$ to rewrite the expression as:

$a = (-1)/-1 xx (-y - z)/(x - w)$

$a = (-1(-y - z))/(-1(x - w))$

$a = (y + z)/(-x + w)$

$a = (y + z)/(w - x)$

How do you solve for a in ax+ z = aw-yax+ z = aw-y?