Q. 12 - Algebra 2

Question

Solve each equation. Check your solution

$\left|2w+3\right|+6=2$

Step-by-Step Solution

Answer

The solutions of the equations is $\mathbf{36}$ or $\mathbf{-}\mathbf{32}$.

Step 1. 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.

Step 2. Solve the equation

Case1

 $\begin{array}{c}a=b\\ 2w+3+6=2\\ 2w=-9+2=-7\\ w=-\frac{7}{2}\end{array}$

Case2

 $\begin{array}{c}a=-b\\ 2w+3+6=-2\\ 2w=-9-2=-11\\ w=-\frac{-11}{2}\end{array}$

Step 3. Check the solutions

Put the value of $w=-\frac{7}{2}$ in equation $\left|2w+3\right|+6=2$.

 Put the value of $y=-32$ in equation $\left|y-2\right|=34$

 $\begin{array}{c}\left|y-2\right|=34\\ \left|-32-2\right|=\left|-34\right|=34\end{array}$

The solution is $36$ or $-32$. Hence the solution set is $\left(-32,36\right)$.