[tex]\begin{gathered} \text{Given} \\ -\frac{5b}{3}-7+\frac{2b}{3}\geq-1 \end{gathered}[/tex]
First, solve for b by moving all the constant on the right side of the inequality, and simplify
[tex]\begin{gathered} -\frac{5b}{3}-7+\frac{2b}{3}\geq-1 \\ -\frac{5b}{3}+\frac{2b}{3}\geq-1+7 \\ \frac{-3b}{3}\geq6 \\ \frac{-\cancel{3}b}{\cancel{3}}\geq6 \\ -b\geq6 \end{gathered}[/tex]
Divide or multiply both sides by -1, to get rid of the negative coefficient of b. Note that dividing or multiplying a negative number "flips" the inequality.
[tex]\begin{gathered} -b\cdot-1\geq6\cdot-1 \\ b\leq-6 \end{gathered}[/tex]
Next, since the solution includes -6, draw a dot on b = -6, and an arrow pointing towards the left. (The inequality also points towards the left)
