Answer
a) $b>3$
b) possible first step: add $1$ to both sides of the inequality
Work Step by Step
a) Using the properties of equality, the solution to the given inequality is
$$\begin{aligned}
3b+12&>27-2b
\\
3b+2b&>27-12
\\
5b&>15
\\
b&>\frac{15}{5}
\\
b&>3
.\end{aligned}
$$
Checking: Substituting any value of $b$ greater than $3$ (such as $b=4$) in the original equality results in
$$\begin{aligned}
3(4)+12&\overset{?}>27-2(4)
\\
12+12&\overset{?}>27-8
\\
24&\overset{\checkmark}>19\text{ (TRUE)}
.\end{aligned}
$$Since the substitution above ended with a TRUE statement, then the solution is indeed $b>3$.
b) In Problem $4$, the first step can also be to add $1$ to both sides of the inequality. It can also be to subtract $6n$ to both sides. Or it can also be to subtract $8$ to both sides. In all of these possibilities, the idea is to isolate the variable on one side.
