Question

Solve each equation. Check your solution

$\left|a-9\right|=20$

Short answer

The solutions of the equations are -11 or 29.

Step-by-step solution

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 $x=y$.
• 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.

Step 2. Solve the equations

Case1

$\begin{array}{c}x=y\\ a-9=20\\ a=20+9\\ =29\end{array}$

Case2

$\begin{array}{c}x=-y\\ a-9=-20\\ a=-20+9\\ =-11\end{array}$

Step 3. Check the solutions

Put the value of $a=29$ in the equation $\left|a-9\right|=20$

$\begin{array}{c}\left|a-9\right|=20\\ \left|29-9\right|=20\end{array}$

Put the value of $a=-11$ in the equation $\left|a-9\right|=20$

$\left|-11-9\right|=\left|-20\right|=20$

The solution is $-11$ or $29$. Hence the solution set is $(-11,29)$.