# How do you solve 3b-6>=15+24b?

May 29, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{3 b}$ and $\textcolor{b l u e}{15}$ from each side of the inequality to isolate the $b$ term while keeping the inequality balanced:

$3 b - 6 - \textcolor{red}{3 b} - \textcolor{b l u e}{15} \ge 15 + 24 b - \textcolor{red}{3 b} - \textcolor{b l u e}{15}$

$3 b - \textcolor{red}{3 b} - 6 - \textcolor{b l u e}{15} \ge 15 - \textcolor{b l u e}{15} + 24 b - \textcolor{red}{3 b}$

$0 - 21 \ge 0 + \left(24 - \textcolor{red}{3}\right) b$

$- 21 \ge 21 b$

Now, divide each side of the inequality by $\textcolor{red}{21}$ to solve for $b$ while keeping the inequality balanced:

$- \frac{21}{\textcolor{red}{21}} \ge \frac{21 b}{\textcolor{red}{21}}$

$- 1 \ge \frac{\textcolor{red}{\cancel{\textcolor{red}{21}}} b}{\cancel{\textcolor{red}{21}}}$

$- 1 \ge b$

To state the solution in terms of $b$ we can reverse or "flip" the entire inequality:

$b \le - 1$