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

Last updated date: 24th Jul 2024
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Hint: Take out all the like terms to one side and all the alike terms to the other side. Take out all the common terms. Reduce the terms on the both sides until they cannot be reduced any further if possible. Then finally evaluate the value of the unknown variable.

Complete step-by-step solution:
 First we will start off by opening the brackets and taking all the like terms to one side.
$ax - aw = - z - y$
Now we will take out any common terms from both sides if possible.
$a(x - w) = - z - y$
Now we will reduce the terms on both the sides.
$a(x - w) = - (z + y)$
Now we simplify our final answer that is evaluate the value of the variable $a$.
\Rightarrow a(x - w) = - (z + y) \\
\Rightarrow a = \dfrac{{ - (z + y)}}{{(x - w)}} \\
\Rightarrow a = \dfrac{{(z + y)}}{{(w - x)}} \\
Hence, the value of $a$ is $\dfrac{{(z + y)}}{{(w - x)}}$.

Note: While taking terms from one side to another, make sure you are changing their respective signs as well. While opening any brackets, always multiply the signs present outside the brackets along with the terms. Reduce the terms using the factorisation method.