Chapter 6.4, Problem 75E

To determine

To solve the equation:

  $6\left(r-2\right)=2r+8$

Also check the solution.

Answer to Problem 75E

  $r=5$

Explanation of Solution

Given:

  $6\left(r-2\right)=2r+8$

Concept Used:

Steps to solve a linear equation:

1. Use distributive property to remove any grouping symbol.
2. Simplify the expression in each side of the equation.
3. Collect the variable terms on one side of the equation and the constant on the other side.
4. Isolate the variable
5. Check the solution by putting the solution in left and right hand and see if they are equal

Calculation:

In order to solve the equation:

  $6\left(r-2\right)=2r+8$

First, collect the variable terms on one side of the equation and the constant on the other side, as

  $\begin{array}{c}6\left(r-2\right)=2r+8\\ 6r-12=2r+8\\ \Rightarrow 6r-2r=8+12\\ \Rightarrow 4r=20\end{array}$

Now, isolate the variable r, as

  $\begin{array}{c}4r=20\\ \Rightarrow \frac{4r}{4}=\frac{20}{4}\\ \Rightarrow r=5\end{array}$

Thus, solution of given equation is $r=5$ .

Now, to check this solution put $r=5$ in left, and right hand side of the given equation, and check whether both sides are equal. Left hand side:

  $\begin{array}{c}6\left(5-2\right)=6\left(3\right)\\ =18\end{array}$

Now, put $r=5$ in right hand side of given equation:

  $\begin{array}{c}2r+8=2\left(5\right)+8\\ =10+8\\ =18\\ =\text{Left hand}\end{array}$

Thus, $r=5$ is correct solution for given equation.