Chapter 1.8, Problem 29E

a.

To determine

To evaluate : the expression $2x+1$ when $x=-3,-2,-1,0,1,2\text{ and }3$ .

Answer to Problem 29E

The values of the expression when $x=-3,-2,-1,0,1,2\text{ and }3$ are $-5,-3,-1,1,3,5,\text{ and }7$ respectively.

Explanation of Solution

Given information :

Consider, the expression provided in the question,

  $2x+1$

Calculation :

To evaluate the expression for $x=-3$ , it is needed to substitute $-3$ for $x$ in expression $2x+1$

Therefore, the value of the expression when $x=-3$ is obtained as:

  $\begin{array}{l}2x+1=2\left(-3\right)+1\\ 2x+1=-6+1\\ 2x+1=-5\end{array}$

Therefore, the value of the expression when $x=-3$ is $-5$ .

Similarly, the value of the expression $2x+1$ when $x=-2$ is obtained as:

  $\begin{array}{l}2x+1=2\left(-2\right)+1\\ 2x+1=-4+1\\ 2x+1=-3\end{array}$

For $x=-1$ the value of the expression is :

  $\begin{array}{l}2x+1=2\left(-1\right)+1\\ 2x+1=-2+1\\ 2x+1=-1\end{array}$

For $x=0$ the value of the expression is :

  $\begin{array}{l}2x+1=2\left(0\right)+1\\ 2x+1=0+1\\ 2x+1=1\end{array}$

For $x=1$ the value of the expression is :

  $\begin{array}{l}2x+1=2\left(1\right)+1\\ 2x+1=2+1\\ 2x+1=3\end{array}$

For $x=2$ the value of the expression is :

  $\begin{array}{l}2x+1=2\left(2\right)+1\\ 2x+1=4+1\\ 2x+1=5\end{array}$

For $x=3$ the value of the expression is :

  $\begin{array}{l}2x+1=2\left(3\right)+1\\ 2x+1=6+1\\ 2x+1=7\end{array}$

Hence,

The values of the expression when $x=-3,-2,-1,0,1,2\text{ and }3$ are $-5,-3,-1,1,3,5,\text{ and }7$ respectively.

b.

To determine

To evaluate : Use the result from part (a) to write a list of ordered pairs in the form $\left(x,2x+1\right)$ .

Answer to Problem 29E

The ordered pair when $x=-3,-2,-1,0,1,2\text{ and }3$ are $\left(-3,-5\right)$

$\left(-2,-3\right)$ , $\left(-1,-1\right)$ , $\left(0,1\right)$ , $\left(1,\text{ 3}\right)$ , $\left(2,\text{ 5}\right)$ and $\left(3,\text{ 7}\right)$ respectively.

Explanation of Solution

Given information :

Consider, the form of ordered pair provided in the question,

  $\left(x,2x+1\right)$

Calculation :

From part (a) the ordered pair when $x=-3$ is $\left(-3,-5\right)$ .

Similarly, the ordered pair when $x=-2,-1,0,1,2\text{ and }3$ are $\left(-2,-3\right)$ , $\left(-1,-1\right)$ , $\left(0,1\right)$ , $\left(1,\text{ 3}\right)$ , $\left(2,\text{ 5}\right)$ and $\left(3,\text{ 7}\right)$ respectively.

Hence,

The ordered pair when $x=-3,-2,-1,0,1,2\text{ and }3$ are $\left(-3,-5\right)$

$\left(-2,-3\right)$ , $\left(-1,-1\right)$ , $\left(0,1\right)$ , $\left(1,\text{ 3}\right)$ , $\left(2,\text{ 5}\right)$ and $\left(3,\text{ 7}\right)$ respectively.

c.

To determine

To plot : The ordered pairs $\left(x,2x+1\right)$ in part (b) in a coordinate plane.

Explanation of Solution

Given information :

The ordered pairs $\left(x,2x+1\right)$ for $x=-3,-2,-1,0,1,2\text{ and }3$ are $\left(-3,-5\right)$

$\left(-2,-3\right)$ , $\left(-1,-1\right)$ , $\left(0,1\right)$ , $\left(1,\text{ 3}\right)$ , $\left(2,\text{ 5}\right)$ and $\left(3,\text{ 7}\right)$ respectively.

Graph :

The graph of the provided ordered pair is sketched below:

d.

To determine

To identify : the graph of part (c) and explain the reason.

Explanation of Solution

Interpretation :

From the graph in part (c) it can be observed that all the points of the ordered pairs $\left(x,2x+1\right)$ lies in the straight line.