Chapter 2.5, Problem 20E

To determine

To solve:the inequality and graph the solution.

Answer to Problem 20E

Therefore, the inequality solution is $b<-3$ or $b\ge 5$

  

Explanation of Solution

Given:

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

Calculation:

Equation $1$ :

  $35<7\left(2-b\right)$

  $35<14-7b$ Use Distributive Property

  $35-14<14-14-7b$ Subtract both sides by $14$

  $\frac{21}{-7}<\frac{-7b}{-7}$ Divide both sides by $-7$

  $-3>b$ Reverse inequality symbol

  $b<-3$

Place inequality symbol on the left side

Equation $2$ :

  $\frac{1}{3}\left(15b-12\right)\ge 21$

  $5b-4\ge 21$ Use Distributive Property

  $5b-4+4\ge 21+4$ Add both sides by $4$

  $\frac{5b}{5}\ge \frac{25}{5}$ Divide both sides by $5$

  $b\ge 5$ Simplify

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:

Therefore, the inequality solution is $b<-3$ or $b\ge 5$