To solve for [tex]\( q \)[/tex] in the equation
[tex]\[
r = \frac{1}{2} s (t + q),
\][/tex]
we can follow these steps:
1. Isolate the term containing [tex]\( q \)[/tex]: Start by clearing the fraction to make the equation easier to work with. We multiply both sides of the equation by 2:
[tex]\[
2r = s (t + q).
\][/tex]
2. Expand the right-hand side: Distribute [tex]\( s \)[/tex] on the right-hand side:
[tex]\[
2r = st + sq.
\][/tex]
3. Isolate [tex]\( q \)[/tex]: We need to get [tex]\( q \)[/tex] alone on one side of the equation. First, subtract [tex]\( st \)[/tex] from both sides to move the [tex]\( st \)[/tex] terms to the left:
[tex]\[
2r - st = sq.
\][/tex]
4. Solve for [tex]\( q \)[/tex]: Divide both sides of the equation by [tex]\( s \)[/tex] to isolate [tex]\( q \)[/tex]:
[tex]\[
q = \frac{2r - st}{s}.
\][/tex]
Therefore, the solution for [tex]\( q \)[/tex] in terms of [tex]\( r \)[/tex], [tex]\( s \)[/tex], and [tex]\( t \)[/tex] is
[tex]\[
q = \frac{2r}{s} - t.
\][/tex]
