Chapter 6.3, Problem 52SR

To determine

To find: The statement best describes the graph of $\left|5-b\right|<2$

Answer to Problem 52SR

Circles on 3 and 7 with shading in between.

Explanation of Solution

Given information:

Natalie solved the inequality $\left|5-b\right|<2$ and graphed it.

Calculation:

  $\left|5-b\right|<2$

We can rewrite it as

  $-2<5-b<2$

Subtract both sides 5

  $\begin{array}{l}-2-5<5-5-b<2-5\\ -7<-b<-3\end{array}$

Divide each by -1 to solve for ‘b’

  $7>b>3$

We can rewrite it as

  $3<b<7$

This compound inequality helps us to select right option.

Conclusion: So, it is a graph of shading in between 3 and 7 and open circles at 3 and 7.