Problem 1 - Elementary Algebra

Question

Evaluate for the given set of \(x\) -values. $$ 252 \times 2 ;\\{-5,0,5\\} $$

Step-by-Step Solution

Answer

The product of 252 and 2 is 504.

Step 1: Understand the Expression

The expression we need to evaluate is \(252 \times 2\). Our goal is simply to find what this expression evaluates to because it does not depend on the set of \(x\)-values. The given \(x\)-values are not relevant to this specific arithmetic expression.

Step 2: Calculate the Product

Calculate the product of the numbers in the expression: \(252 \times 2 = 504\).

Step 3: Confirmation

Verify the calculation by checking the multiplication again. When re-calculated, \(252 \times 2\) indeed equals \(504\), confirming our evaluation.

Key Concepts

Multiplication

Multiplication is one of the most fundamental arithmetic operations. It involves finding the total number when you have several groups of the same size. In the expression provided, we see:

• The numbers: 252 and 2,
• The operation: Multiplication (denoted by the symbol \( \times \)).

This operation means adding the number 252, two times, as shown here: \[ 252 + 252 \]. Multiplying any number by 2 is often seen as doubling that number. It's a quick way to increase a quantity and is frequently an integral part of more complex mathematical problems. Knowing basic multiplication facts, like the one given here, ensures efficiency in solving such tasks. When you multiply, start by writing the numbers vertically if needed, aligning them by their place value. Begin with the units digit, multiplying each digit of the first number by the second, carrying over if necessary. This step-by-step approach helps confirm your results.

Problem Solving

Problem solving in mathematics often requires a clear understanding of the problem at hand. In this case, we had to evaluate the expression \(252 \times 2\). Here are a few tips to help with mathematical problem solving:

• Read carefully: Understand what is being asked.
• Identify the operation: Know which mathematical operations you'll use; multiplication in this instance.
• Check your work: Always verify your results.

In our problem, the expression did not rely on the provided set of \(x\)-values \(\{-5, 0, 5\}\). The values of \(x\) were extraneous, as they do not tie into bereaved expression. This highlights that part of problem solving is recognizing irrelevant information. Staying focused on only what's necessary can save time and confusion, especially in algebra where expressions may sometimes misconstrue the context.

Evaluation of Expressions

Evaluating expressions involves systematically calculating there's a value based on the numbers and operations present. Here, we only had to deal with the expression \(252 \times 2\). To properly evaluate such expressions:

• Identify the operation: Know what you need to do, in this case, multiply.
• Carry out the computation: Perform the calculations accurately.
• Verify the results: Re-do the calculation if necessary, to confirm.

In our solution, we carried out the multiplication: \[ 252 \times 2 = 504 \]. Double-checked the work and confirmed the result was correct. When evaluating expressions, verifying calculations can prevent errors, especially in complex equations. This precision is crucial across all expressions to ensure valid and reliable outcomes.