Q31. - Algebra 2

Question

 Solve each equation. Check your solution

$\left|a+12\right|=33$

Step-by-Step Solution

Answer

The solutions of the equations is 21 or -45

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 x=y 
• Secondly assume the case two in which the equation be x=-y
• 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- x =y

$\begin{array}{c}a+12=33\\ a=33-12\\ =21\end{array}$

Case2-x=-y

$\begin{array}{c}a+12=-33\\ a=-12-33\\ =-45\end{array}$

Step3- Check the solutions

Put the value of a=-45 in the equation$|a+12|=33$

$\begin{array}{c}|a+12|=|-45+12|\\ =|-33|\\ =33\end{array}$

Put the value of a=21  in equation$|a+12|=33$

$\begin{array}{c}|a+12|=|21+12|\\ =\left|33\right|\\ =33\end{array}$

The solution is21  or-45 . Hence, the solution set is (21-45).