Chapter 8.3, Problem 22HP

To determine

Compare and contrast how to solve the equations $\frac{x+4}{5}=20\text{and}\frac{x}{5}+4=20$

Answer to Problem 22HP

The solutions of the equations $\frac{x+4}{5}=20\text{and}\frac{x}{5}+4=20$ are x = 96 and x = 80

Explanation of Solution

Given:

Compare and contrast how to solve the equations $\frac{x+4}{5}=20\text{and}\frac{x}{5}+4=20$

Concept Used:

Compare and contrast' is a technique to make students aware of mathematical properties and applications. It is effective for learning about subtle sameness’s and differences.

When you compare you identify what is the same, when you contrast you identify what is different.

Both the equations $\frac{x+4}{5}=20\text{and}\frac{x}{5}+4=20$ are linear equation with one variable.

Calculation:

Step 1: For the equation $\frac{x+4}{5}=20$ multiply both sides by 5 and then subtract 4 from both sides.

  $\begin{array}{l}\frac{x+4}{5}=20\\ 5·\frac{x+4}{5}=5·20\text{[ Multiply both sides by 5 ] }\\ x+4=100\\ x+4-4=100-4[\text{Subtract 4 from both sides ] }\\ x=96\end{array}$

Step 1: For the equation $\frac{x}{5}+4=20$ subtract 4 from both sides and then multiply both sides by 5.

  $\begin{array}{l}\frac{x}{5}+4=20\\ \frac{x}{5}+4-4=20-4[\text{Subtract 4 from both sides ] }\\ \frac{x}{5}=16\\ 5·\frac{x}{5}=5·16\text{[ Multiply both sides by 5 ]}\\ x=80\end{array}$

They both are linear equation with one variable.

The difference:

For the equation $\frac{x+4}{5}=20$ multiply both sides by 5 and then subtract 4 from both sides.

For the equation $\frac{x}{5}+4=20$ subtract 4 from both sides and then multiply both sides by 5.

Thus, the solutions of the equations $\frac{x+4}{5}=20\text{and}\frac{x}{5}+4=20$ are x = 96 and x = 80