Q37. - Algebra 2

Question

Solve each equation. Check your solution

$7\left|4x-13\right|=35$

Step-by-Step Solution

Answer

The solutions of the equations is 2 or 4.5

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:$a=b$

$\begin{array}{c}28x-91=35\\ 28x=91+35\\ x=\frac{126}{28}\\ =4.5\end{array}$

Case2:$a=-b$

$\begin{array}{c}28x-91=-35\\ 28x=91-35\\ x=\frac{56}{28}\\ =2\end{array}$

Step3- Check the solutions

Put the value of x=2 in the equation $7\left|4x-13\right|=35$

$\begin{array}{c}7|4x-13|=7|4\times 2-13|\\ =7|8-13|\\ =7\times 5\\ =35\end{array}$

Put the value of x=4.5 in the equation $7\left|4x-13\right|=35$

$\begin{array}{c}7|4x-13|=7|4\times 4.5-13|\\ =7\times 5\\ =35\end{array}$

The solution is 2 or 4.5.