Chapter 1.3, Problem 5ST

To determine

To solve: the equation $12-2x=2$ .

Answer to Problem 5ST

  $x=5$

Explanation of Solution

Given:

  $x\in \left\{0,1,2,3,4,5\right\}$

Calculation:

First substitute $x=0$ ,

  $\begin{array}{c}\Rightarrow 12-2\left(0\right)\\ \Rightarrow 12-0\\ \Rightarrow 12\end{array}$

But $12\ne 2$

So, False

Now substitute $x=1$ ,

  $\begin{array}{c}\Rightarrow 12-2\left(1\right)\\ \Rightarrow 12-2\\ \Rightarrow 10\end{array}$

But $10\ne 2$

So, False

Now substitute $x=2$ ,

  $\begin{array}{c}\Rightarrow 12-2\left(2\right)\\ \Rightarrow 12-4\\ \Rightarrow 8\end{array}$

But $8\ne 2$

So, False

Now substitute $x=3$ ,

  $\begin{array}{c}\Rightarrow 12-2\left(3\right)\\ \Rightarrow 12-6\\ \Rightarrow 6\end{array}$

But $6\ne 2$

So, False

Now substitute $x=4$ ,

  $\begin{array}{c}\Rightarrow 12-2\left(4\right)\\ \Rightarrow 12-8\\ \Rightarrow 4\end{array}$

But $4\ne 2$

So, false

Now substitute $x=5$ ,

  $\begin{array}{c}\Rightarrow 12-2\left(5\right)\\ \Rightarrow 12-10\\ \Rightarrow 2\end{array}$

As $2=2$

So, True

Thus, the solution of the given equation is $x=5$ .