Q67. - Algebra 2

Question

Solve each equation. Check your solutions.

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

Step-by-Step Solution

Answer

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

Step 1 – 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 $p=-q$

Step 2 – 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.

Step 3 – 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 $\varnothing$.