Chapter 1.3, Problem 7WE

To determine

To solve: The equation if solution is member of given set.

Answer to Problem 7WE

The required solution of equation $2x=8$ is $x=4$ such that $x\in \left\{0,1,2,3,4,5\right\}$

Explanation of Solution

Given information:

The equation $2x=8$ has solution $x\in \left\{0,1,2,3,4,5\right\}$ .

Formula used:

The solution of equation $ax=b$ is given by $\frac{ax}{a}=\frac{b}{a}\Rightarrow x=\frac{b}{a}$ .

Calculations:

The given equation is

  $2x=8$.............(1)

Dividing both sides of equation (1) by 2

  $\frac{2x}{2}=\frac{8}{2}$

  $\Rightarrow \frac{\cancel{2}x}{\cancel{2}}=\frac{\stackrel{4}{\cancel{8}}}{\cancel{2}}$

  $\Rightarrow x=4$

Now, since $4\in \left\{0,1,2,3,4,5\right\}\Rightarrow x\in \left\{0,1,2,3,4,5\right\}$ .

Thus, $x=4$ is the required solution of the equation $0=4x$ .

Conclusion:

The required solution of equation $2x=8$ is $x=4$ such that $x\in \left\{0,1,2,3,4,5\right\}$ .