Solve for X:
X=
Z - Y
\large{X + Y = Z}
Subtract
abs(Y)
from both sides of
the equation to get X by itself on
the left.
Add
abs(Y)
to both sides of
the equation to get X by itself on
the left.
\qquad\large{\begin{eqnarray}
X &Y_SIGN abs(Y)
&\quad=\quad&
Z\\
&\pink{Y_SIGNINV abs(Y)}
&&
\pink{Y_SIGNINVabs(Y)}\\
\end{eqnarray}}
\qquad\large{
X\gray{ + 0} \quad=\quadZ - Y
}
Simplifying, X = Z - Y.
\large{Z = X + Y}
Subtract
abs(Y)
from both sides of
the equation to get X by itself on
the right.
Add
abs(Y)
to both sides of
the equation to get X by itself on
the right.
\qquad\large{\begin{eqnarray}
Z
&\quad=\quad&
X &Y_SIGN abs(Y)\\
\pink{Y_SIGNINV abs(Y)}
&&
& \pink{Y_SIGNINVabs(Y)}\\
\end{eqnarray}}
\qquad\large{
Z - Y \quad=\quad X\gray{ + 0}
}
Simplifying, X = Z - Y.
\large{Y + X = Z}
Subtract
abs(Y)
from both sides of
the equation to get X by itself on
the left.
Add
abs(Y)
to both sides of
the equation to get X by itself on
the left.
\qquad\large{\begin{eqnarray}
Y &+\enspace X
&\quad=\quad&
Z\\
\pink{Y_SIGNINV abs(Y)}&
&&
\pink{Y_SIGNINVabs(Y)}\\
\end{eqnarray}}
\qquad\large{
\gray{0 + {}}X \quad=\quadZ - Y
}
Simplifying, X = Z - Y.
\large{Z = Y + X}
Subtract
abs(Y)
from both sides of
the equation to get X by itself on
the right.
Add
abs(Y)
to both sides of
the equation to get X by itself on
the right.
\qquad\large{\begin{eqnarray}
Z
&\quad=\quad&
Y + X\\
\pink{Y_SIGNINV abs(Y)}
&&
\pink{Y_SIGNINVabs(Y)} \\
\end{eqnarray}}
\qquad\large{\begin{eqnarray}
Z
&\quad=\quad&
Y + X\\
\pink{Y_SIGNINV abs(Y)}
&&
\pink{\llap{Y_SIGNINV}abs(Y)} \\
\end{eqnarray}}
\qquad\large{
Z - Y \quad=\quad \gray{0 + }X
}
Simplifying, X = Z - Y.