Chapter 1.3, Problem 26WE

To determine

To find: A number 4 times of which is 6 more than the number. The number is member of the set $\left\{0,2,4,6,8\right\}$

Answer to Problem 26WE

The required number is 2.

Explanation of Solution

Given information:

Four times of the given number is 6 more than the number itself, and the number belongs the set $\left\{0,2,4,6,8\right\}$ .

Formula used:

From the given condition, obtain a lines equation in one variable and solve it.

Calculations:

Let the given number is x and $x\in \left\{0,2,4,6,8\right\}$ .

According to given condition, 4 times of x is 6 more than x

  $4x=x+6$ ............. (1)

Now, we solve, equation (1) as:

  $4x-x=x+6-x$

Subtracting x from each side

  $\Rightarrow 3x=\cancel{x}+6-\cancel{x}$

  $\Rightarrow 3x=6$

Multiplying each side by $\frac{1}{3}$

  $\Rightarrow \cancel{3}x\times \frac{1}{\cancel{3}}=\stackrel{2}{\cancel{6}}\times \frac{1}{\cancel{3}}$

  $\Rightarrow x=2$

Now, since $2\in \left\{0,2,4,6,8\right\}\Rightarrow x\in \left\{0,2,4,6,8\right\}$ .

Thus, $x=2$ is the required number?

Test: $4\times 2=2+6$

Conclusion:

The required number is 2.