Question

Hello! I got this question wrong. Can we work through it to see what I should have done?

Answer 1

`\begin{gathered} \text{Given} \\ -(5b)/(3)-7+(2b)/(3)\geq-1 \end{gathered}`

First, solve for b by moving all the constant on the right side of the inequality, and simplify

`\begin{gathered} -(5b)/(3)-7+(2b)/(3)\geq-1 \\ -(5b)/(3)+(2b)/(3)\geq-1+7 \\ (-3b)/(3)\geq6 \\ \frac{-\cancel{3}b}{\cancel{3}}\geq6 \\ -b\geq6 \end{gathered}`

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.

`\begin{gathered} -b\cdot-1\geq6\cdot-1 \\ b\leq-6 \end{gathered}`

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)