To solve for the variable [tex]\( r \)[/tex] in the given equation [tex]\( q = \frac{c}{4}(h + r) \)[/tex], follow these steps:
1. Clear the fraction:
Multiply both sides of the equation by 4 in order to eliminate the fraction.
[tex]\[
4q = c(h + r)
\][/tex]
2. Isolate the term containing [tex]\( r \)[/tex]:
To isolate [tex]\( r \)[/tex], divide both sides of the equation by [tex]\( c \)[/tex].
[tex]\[
\frac{4q}{c} = h + r
\][/tex]
3. Solve for [tex]\( r \)[/tex]:
Subtract [tex]\( h \)[/tex] from both sides of the equation to isolate [tex]\( r \)[/tex].
[tex]\[
r = \frac{4q}{c} - h
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{d. \ r = \frac{4q}{c} - h}
\][/tex]
