Certainly! Let's solve the equation [tex]\( A = \frac{1}{3} h (q + z) \)[/tex] for the variable [tex]\( q \)[/tex]. We'll follow a step-by-step approach:
1. Clear the fraction:
Start by eliminating the fraction by multiplying both sides of the equation by 3:
[tex]\[
3A = h (q + z)
\][/tex]
2. Isolate the term containing [tex]\( q \)[/tex]:
Next, we need to isolate the term containing [tex]\( q \)[/tex]. To do this, divide both sides of the equation by [tex]\( h \)[/tex]:
[tex]\[
\frac{3A}{h} = q + z
\][/tex]
3. Solve for [tex]\( q \)[/tex]:
Finally, isolate [tex]\( q \)[/tex] by subtracting [tex]\( z \)[/tex] from both sides of the equation:
[tex]\[
q = \frac{3A}{h} - z
\][/tex]
Therefore, the solution for [tex]\( q \)[/tex] is:
[tex]\[
q = \frac{3A}{h} - z
\][/tex]
