Solve for z: 8z + 12 = 44.

To solve the equation (8z + 12 = 44), the first step is to isolate the term containing (z). This is done by subtracting 12 from both sides of the equation:

[

8z + 12 - 12 = 44 - 12

]

This simplifies to:

[

8z = 32

]

Next, to find the value of (z), divide both sides of the equation by 8:

[

z = \frac{32}{8}

]

This further simplifies to:

[

z = 4

]

Thus, the solution to the equation is (z = 4), which corresponds to the correct answer. The process involved basic algebraic operations—subtracting and dividing—which are essential skills in solving linear equations. Understanding this kind of problem helps reinforce the concept of isolating variables to find their values.