Question

Solve each equation. Check your solution.

$\left|\mathbf{8}\mathbf{\omega }\mathbf{+}\mathbf{2}\right|\mathbf{+}\mathbf{2}\mathbf{=}\mathbf{0}$

Short answer

The solution set of given equation is $\varnothing$.

Step-by-step solution

– Description of step.

For any real numbers p and q, where $q\ge 0$,

Case 1) if $\left|p\right|=q$then $p=q$or

Case 2) if $\left|p\right|=q$then $p=-q$

– Description of step.

Subtract 2 from both the sides of the given equation.

$\begin{array}{c}\left|8\omega +2\right|+2-2=0-2\\ \left|8\omega +2\right|=-2\end{array}$

– Description of step.

The given equation is $\left|8\omega +2\right|=-2$. This statement is not true since, the absolute value of a real number is non-negative irrespective of its sign.

– Description of step.

The statement $\left|8\omega +2\right|=-2$ is not true and hence the solution is $\varnothing$.

Therefore, the solution set of given equation is data-custom-editor="chemistry" $\varnothing$.