Chapter 2.5, Problem 20E

To determine

To calculate: The inequality using the graph.

Answer to Problem 20E

The graph is open point at -3 and a shaded line going to the left of -3 and a closed point at 5 and a shaded line going to the right of 5.

Explanation of Solution

Given information:

The given inequality equation as given below,

  $35<7\left(2-b;or\frac{1}{3}\left(15b-12\right)\ge 21\right)$

Formula used:

Distributive property is used.

Calculation:

The operations are applied to all sides of the compound inequality. With multiplication and division of negative numbers be sure to reverse the inequality symbol after applying the operation.

a. compound inequality.

  $\begin{array}{l}35<7\left(2-b\right)\\ 35<14-7b\end{array}$

Use Distributive Property Subtract both sides by 14

  $35-14<14-14-7b$

Divide both sides by -7

  $\frac{21}{-7}<\frac{-7b}{-7}$

Reverse inequality symbol Place inequality symbol on the left side

  $\begin{array}{l}-3>b\\ b<-3\end{array}$

  $\begin{array}{l}\frac{1}{3}\left(15b-12\right)\ge 21\\ 5b-4>21\end{array}$

Use Distributive Property Add both sides by 4

  $5b-4+4\ge 21+4$

Divide both sides by 5

  $\frac{5b}{5}\ge \frac{25}{5}$

Simplify

  $b\ge 5$

Its graph should have an open point at -3 and a shaded line going to the left of -3 and a closed point at 5 and a shaded line going to the right of 5, as in:

  

Conclusion:

The graph is open point at -3 and a shaded line going to the left of -3 and a closed point at 5 and a shaded line going to the right of 5.