Chapter 1.3, Problem 10OE

To determine

To translate: given statement and then find the solution.

Answer to Problem 10OE

  $x=3$

Explanation of Solution

Given information: eight times the sum of 4 and a number is 56 and over the domain $\left\{1,3,5,7,9\right\}$

Calculation:

The required translation of the word statement is as follows:

  $8\left(4+x\right)=56$

Solve for $x=1$ , to get

  $\begin{array}{c}8\left(4+1\right)=56\\ 8\left(5\right)=56\\ 40\ne 56\end{array}$

So given value is false.

Solve for $x=3$ , to get

  $\begin{array}{c}8\left(4+3\right)=56\\ 8\left(7\right)=56\\ 56=56\end{array}$

So given value is true.

Solve for $x=5$ , to get

  $\begin{array}{c}8\left(4+5\right)=56\\ 8\left(9\right)=56\\ 72\ne 56\end{array}$

So given value is true.

Solve for $x=7$ , to get

  $\begin{array}{c}8\left(4+7\right)=56\\ 8\left(11\right)=56\\ 88\ne 56\end{array}$

So given value is false.

Solve for $x=9$ , to get

  $\begin{array}{c}8\left(4+9\right)=56\\ 8\left(13\right)=56\\ 104\ne 56\end{array}$

So given value is false.

Therefore, for given equation, the solution is $x=3$ .