Question

Solve each equation. Check your solution

$-12\left|9x+1\right|=144$

Short answer

The solutions of the equations is$\left(\varphi \right)$

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-$a=b$

$\begin{array}{c}-12(9x+1)=144\\ -108x-12=144\\ -108x=144+12\\ x=-\frac{156}{108}\\ =-1.44\end{array}$

Case2-$a=-b$

$\begin{array}{c}-12(9x+1)=-144\\ -108x-12=-144\\ -108x=-144+12\\ x=\frac{132}{108}\\ =1.22\end{array}$

Step3- Check the solutions

Put the value of x=1.22 in the equation $-12\left|9x+1\right|=144$

$\begin{array}{c}-12|9x+1|=-12|9\times \frac{132}{108}+1|\\ =-12|9\times 1.22+1|\\ =-12\times 11.98\\ =-144\end{array}$

This is not a true solution.

Put the value of x=-1.44 in the equation $-12\left|9x+1\right|=144$

$\begin{array}{c}-12|9\times -1.44+1|=-12|-11.96|\\ =-144\end{array}$

This is not a true solution.

As the modulus value of expression is negative it is not true solution. The solution is $(\varnothing )$.