Chapter 1.5, Problem 58PPS

To determine

To prepare:A table for the values obtained by given replacement set and the equation.

Answer to Problem 58PPS

$x$	$y=3x-2$	$y$
$-2$	$-2\left(-2\right)-3=y$	$1$
$-1$	$-2\left(-1\right)-3=y$	$-1$
$0$	$-2\left(0\right)-3=y$	$-3$
$1$	$-2\left(1\right)-3=y$	$-5$
$2$	$-2\left(2\right)-3=y$	$-7$

Explanation of Solution

Given information:

  $-2x-3=y$

Replacement set $=\left\{-2,-1,0,1,2\right\}$

Calculation:

Let’s substitute the values of replacement set $\left\{-2,-1,0,1,2\right\}$ one by one in the equation-

at $x=-2$ ,

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

at $-1$ ,

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

at 0,

  $\begin{array}{l}-2x-3=y\\ \Rightarrow -2\left(0\right)-3=y\\ \Rightarrow y=-3\end{array}$

at 1,

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

at 2,

  $\begin{array}{l}-2x-3=y\\ \Rightarrow -2\left(2\right)-3=y\\ \Rightarrow y=-7\end{array}$

Therefore, the table will be given as-

$x$	$y=3x-2$	$y$
$-2$	$-2\left(-2\right)-3=y$	$1$
$-1$	$-2\left(-1\right)-3=y$	$-1$
$0$	$-2\left(0\right)-3=y$	$-3$
$1$	$-2\left(1\right)-3=y$	$-5$
$2$	$-2\left(2\right)-3=y$	$-7$