Question

Solve each equation. Check your solution

$\left|x+4\right|=7$

Short answer

The solutions of the equation $\left|x+4\right|=7$is3 or -11

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

Case-1

$\begin{array}{c}a=b\\ x+4=7\\ x=7-4\\ x=3\end{array}$

Case-2

$\begin{array}{c}a=-b\\ x+4=-7\\ x=-7-4\\ x=-11\end{array}$

Step3- Check the solutions

Putting the values of x=3 in equation $\left|x+4\right|=7$

$\begin{array}{c}|3+4|=\left|7\right|\\ =7\end{array}$

Putting the value of x=-11 in equation $\left|x+4\right|=7$

$\begin{array}{c}|-11+4|=|-7|\\ =7\end{array}$

The solutions is3or-11 . Hence, the solution set is (3,-11).