Chapter 1.3, Problem 30E

To determine

To find the value of r in equation:

$4\left(x-3\right)-r+2x=5\left(3x-7\right)-9x$

Answer to Problem 30E

$r=23$

Explanation of Solution

Given:

$4\left(x-3\right)-r+2x=5\left(3x-7\right)-9x$

Concept Used:

• An equation that has two or more than two variables is called a literal equation.
• Steps to solve a literal equation for a variable x :
1. Use distributive property to remove any grouping symbol.
2. Simplify the expression in each side of the equation.
3. Collect the variable terms x on one side of the equation and rest on the other side.
4. Isolate the variable.

Calculation:

In order to find the value of r in equation:

$4\left(x-3\right)-r+2x=5\left(3x-7\right)-9x$

First, simplify the expression in each side of the equation, as

  $\begin{array}{c}4\left(x-3\right)-r+2x=5\left(3x-7\right)-9x\\ 4x-12-r+2x=15x-35-9x\\ 6x-12-r=6x-35\end{array}$

Now, collect the variable terms of r on one side of the equation and rest on the other side, as

$\begin{array}{c}6x-12-r=6x-35\\ \Rightarrow -r=6x-35-6x+12\\ \Rightarrow -r=0-23\\ \Rightarrow -r=-23\\ \Rightarrow 23=r\\ \Rightarrow r=23\end{array}$

Thus,

$r=23$