Chapter 1.5, Problem 14PPS

To determine

To find:Solution set for the given equation.

Answer to Problem 14PPS

  $\left\{7\right\}$

Explanation of Solution

Given information:

  $17=24-y$

Replacement set $=\left\{1,3,5,7,9\right\}$

Replacement set $=\left\{10,12,14,16,18\right\}$

Calculation:

Let’s substitute the values of replacement set $\left\{1,3,5,7,9\right\}$ one by one in the equation-

at 1,

  $\begin{array}{l}17=24-y\\ \Rightarrow 17=24-1\\ \Rightarrow 17=23\left(\text{False}\right)\end{array}$

at 3,

  $\begin{array}{l}17=24-y\\ \Rightarrow 17=24-3\\ \Rightarrow 17=21\left(\text{False}\right)\end{array}$

at 5,

  $\begin{array}{l}17=24-y\\ \Rightarrow 17=24-5\\ \Rightarrow 17=19\left(\text{False}\right)\end{array}$

at 7,

  $\begin{array}{l}17=24-y\\ \Rightarrow 17=24-7\\ \Rightarrow 17=17\left(\text{True}\right)\end{array}$

at 9,

  $\begin{array}{l}17=24-y\\ \Rightarrow 17=24-9\\ \Rightarrow 17=15\left(\text{False}\right)\end{array}$

Let’s substitute the values of replacement set $\left\{10,12,14,16,18\right\}$ one by one in the equation-

at 10,

  $\begin{array}{l}17=24-y\\ \Rightarrow 17=24-10\\ \Rightarrow 17=14\left(\text{False}\right)\end{array}$

at 12,

  $\begin{array}{l}17=24-y\\ \Rightarrow 17=24-12\\ \Rightarrow 17=12\left(\text{False}\right)\end{array}$

at 14,

  $\begin{array}{l}17=24-y\\ \Rightarrow 17=24-14\\ \Rightarrow 17=10\left(\text{False}\right)\end{array}$

at 16,

  $\begin{array}{l}17=24-y\\ \Rightarrow 17=24-16\\ \Rightarrow 17=8\left(\text{False}\right)\end{array}$

at 18,

  $\begin{array}{l}17=24-y\\ \Rightarrow 17=24-18\\ \Rightarrow 17=6\left(\text{False}\right)\end{array}$

Therefore, the solution set is $\left\{7\right\}$