Chapter 12.5, Problem 9MRE

To determine

To calculate: The value of x in simplified form for the equation

  $2\left(x+4\right)\left(x+7\right)=\left(2x+1\right)\left(x-9\right)-3$ .

Answer to Problem 9MRE

The value of x in simplified formis $-\frac{68}{39}$ .

Explanation of Solution

Given information:

The equation $2\left(x+4\right)\left(x+7\right)=\left(2x+1\right)\left(x-9\right)-3$ .

Calculation:

Consider the equation $2\left(x+4\right)\left(x+7\right)=\left(2x+1\right)\left(x-9\right)-3$ .

Multiply the terms in the bracket on both sides of the equation.

  $\begin{array}{c}2\left(x+4\right)\left(x+7\right)=\left(2x+1\right)\left(x-9\right)-3\\ 2\left[x^2+4x+7x+28\right]=2x^2-18x+x-9-3\\ 2x^2+22x+56=2x^2-17x-12\end{array}$

Take all terms on left hand side and simplify,

  $\begin{array}{c}2x^2+22x+56-2x^2+17x+12=0\\ 39x+68=0\\ 39x=-68\\ x=-\frac{68}{39}\end{array}$

Thus, the value of x in simplified form is $-\frac{68}{39}$ .