Chapter 1.3, Problem 12WE

To determine

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

Answer to Problem 12WE

The required solution of equation $0=4x$ is $x=0$ .

Explanation of Solution

Given information:

The equation $0=4x$ 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

  $0=4x$

  $\Rightarrow 4x=0$ ..............(1)

Dividing both sides of equation (1) by 4

Or multiplying both sides of equation (1) by inverse of 4 that is by $\frac{1}{4}$ , we have

  $4\cdot x\cdot \frac{1}{4}=0\cdot \frac{1}{4}$

  $\Rightarrow x\cdot \left(4\cdot \frac{1}{4}\right)=0$$\because 0\cdot \frac{1}{4}=0$

  $\Rightarrow x\cdot 1=0$$\because 4\cdot \frac{1}{4}=1$

  $\Rightarrow x=0$ .

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

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

Conclusion:

The required solution of equation $0=4x$ is $x=0$ .