Question

Solve each equation. Check your solution

$-3\left|2n+5\right|=-9$

Short answer

The solutions of the equations is-1 or -4

Step-by-step solution

Step1- Order for solving the equation

To evaluate any equation involving more than one operation, follow the below order operation

• First assume the case one in which the equation be a=b.
• Secondly assume the case two in which the equation be a=-b.
• Solve the equations of both the cases to find the value of algebraic expression
• After finding the two values of algebraic expression, put the value in the original equation and check the solution

Step2- Solve the equations  

Case1- $a=b$

$\begin{array}{c}-3(2n+5)=-9\\ -6n-15=-9\\ -6n=-9+15\\ -n=\frac{6}{6}\\ n=-1\end{array}$

Case2- $a=-b$

$\begin{array}{c}-3(2n+5)=-(-9)\\ -6n-15=9\\ -6n=15+9\\ n=-\frac{24}{6}\\ =-4\end{array}$

Step3- Check the solutions

Put the value of n=-1 in the equation $-3\left|2n+5\right|=-9$

$\begin{array}{c}-3|2n+5|=-3|2\times -1+5|\\ =-3\left|3\right|\\ =-9\end{array}$

Put the value of n=-4 in the equation $-3\left|2n+5\right|=-9$

$\begin{array}{c}-3|2\times -4+5|=-3|-8+5|\\ =-3|-3|\\ =-9\end{array}$

The solution is -1 or -4. Hence, the solution set is $\left(-4,-1\right)$.