Question

Solve each equation. Check your solutions.

67. $\left|\mathbf{8}\mathbf{c}\mathbf{+}\mathbf{7}\right|\mathbf{=}\mathbf{-}\mathbf{4}$

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.

The given equation is $\left|8c+7\right|=-4$. 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 $\left|8c+7\right|=-4$is not true and hence the solution is $\varnothing$.

Therefore, the solution set of given equation is $\varnothing$.