Question

Solve each equation. Check your solution

$\left|3x+5\right|=11$

Short answer

The solutions of the equations is2 or$\frac{-16}{3}$

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- $a=b$

$\begin{array}{c}3x+5=11\\ 3x=11-5\\ x=\frac{6}{3}\\ =2\end{array}$

Case2- $a=-b$

$\begin{array}{c}3x+5=-11\\ 3x=-11-5\\ x=-\frac{16}{3}\end{array}$

Step3- Check the solutions

Put the value of x=2 in the equation $\left|3x+5\right|=11$

$\begin{array}{c}|3x+5|=|3\times 2+5|\\ =11\end{array}$

Put the value of $x=\frac{-16}{3}$ in equation $\left|3x+5\right|=11$

$\begin{array}{c}|3x+5|=|3\times -\frac{16}{3}+5|\\ =|-11|\\ =11\end{array}$

The solution is 2 or $\frac{-16}{3}$. Hence, the solution set is $\left(2,\frac{-16}{3}\right)$.