How do you solve the inequality 8z + 3 < 2z + 51?

To solve the inequality 8z + 3 < 2z + 51, start by isolating the variable z on one side of the inequality.

First, we want to get all the terms involving z on one side. Subtract 2z from both sides:

8z - 2z + 3 < 51

This simplifies to:

6z + 3 < 51

Next, subtract 3 from both sides:

6z < 51 - 3

This becomes:

6z < 48

Now, divide both sides by 6:

z < rac{48}{6}

This results in:

z < 8

So, the solution to the inequality is z < 8. This means that any value of z less than 8 will satisfy the original inequality.