Chapter 3.1, Problem 10MRE

a

To determine

To solve: $\left|3-m\right|>1$ .

Answer to Problem 10MRE

Solution is $m>4$ or $m<2$ .

Explanation of Solution

Given Information: An open sentence is given that is $\left|3-m\right|>1$ where, m is a variable

Calculation:

To solve $\left|3-m\right|>1$ , make two cases:

Case 1: When $3-m$ > 0, then we have

  $3-m>1$

Or  $-m>-2$

  $m<2$ ............(1)

Case 2: When $3-m$< 0, then we have

  $-3+m>1$

Or  $m>4$ ............(2)

b

To determine

To draw: The graph for the solution set of $\left|3-m\right|>1$

Explanation of Solution

Given Information: By solving the above inequality we have obtained the 2 conditions that is, $m<2$ or $m>4$

Graph: We need to sketch the graph of $m<2$ and $m>4$

  

Interpretation: We can see from the graph above, that the red coloured region shows the solution set of $m<2$ .

And the blue coloured region shows the solution set of $m>4$ .