Problem 121 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although I can solve \(3 x+\frac{1}{5}=\frac{1}{4}\) by first subtracting \(\frac{1}{5}\) from both sides, I find it easier to begin by multiplying both sides by \(20,\) the least common denominator.

Step-by-Step Solution

Answer

The statement does not make sense. Multiplying by 20 first leads to a different, incorrect answer.

Step 1 - Understand the problem

The first step is to understand the meaning of the statement. It's proposing a new way of solving the equation, that is multiplying the equation by 20 before other operations.

Step 2 - Apply the process

Apply the method to the equation. Multiply both sides of the equation by 20 to clear the fraction: \(20(3x + \frac{1}{5}) = 20*\frac{1}{5}\). This will give: \(60x + 4 = 1\)

Step 3 - Compare with standard method

Compare this with the standard method of solving this type of equation: first subtract \(\frac{1}{5}\) from both sides, then multiply by \(20\). The standard method yields: \(3x = \frac{1}{5} - \frac{1}{5}\) then \(60x = 0\).

Step 4 - Evaluate the statement

Looking at these two methods, it's clear that the method described in the statement does not lead to the correct solution. Thus, the statement does not make sense.