Problem 39 - Elementary Algebra

Question

For the following problems, state whether the given statements are the same or different. Represent the product of 3 and \(x\) five different ways.

Step-by-Step Solution

Answer

Question: List five different ways to represent the product of 3 and x. Answer: The product of 3 and x can be represented in the following ways: 1. \(3x\) 2. \((3)(x)\) 3. \(3 \cdot x\) 4. \(3\frac{x}{1}\) 5. \(3f(x)\), where \(f(x) = x\)

Step 1: 1. Traditional multiplication notation

We can represent the product of 3 and x as \(3x\). This is the most common way to write the multiplication of a constant and a variable.

Step 2: 2. Using parentheses

Another way to represent the product is by using parentheses. We can write it as \((3)(x)\), which means the same as \(3x\).

Step 3: 3. Using a dot for multiplication

We can also use a dot to indicate multiplication. In this case, the expression can be written as \(3 \cdot x\). This notation is often used in mathematics to represent multiplication.

Step 4: 4. Using a fraction

We can also represent the product of 3 and x by using a fraction. We can write it as \(3 \frac{x}{1}\). Since any number divided by 1 is itself, this expression is equivalent to \(3x\).

Step 5: 5. Implicit multiplication with a function

Finally, we can represent the product of 3 and x using an implicit multiplication with a function. For example, we can define a function \(f(x) = 3x\) and then write the expression as \(3f(x)\), which will still represent the product of 3 and x. So, using these five different ways, we have represented the product of 3 and x as follows: 1. \(3x\) 2. \((3)(x)\) 3. \(3 \cdot x\) 4. \(3\frac{x}{1}\) 5. \(3f(x)\), where \(f(x) = x\)