Problem 8 Which of the following is equiva... [FREE SOLUTION] (2024)

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To simplify algebraic expressions, finding common factors is essential. It helps in breaking down expressions into simpler and more manageable forms. For instance, in the expression \(5x - 20\), we need to identify a number that both terms, 5x and 20, share. This number is known as the common factor. In this case, the common factor is 5. By factoring out 5, we rewrite the expression as \(5(x - 4)\). This step not only simplifies the expression but also makes it easier to work with in equations or further simplifications.

Always look for the greatest common factor that can be factored out from all terms. It helps in reducing the complexity of the algebraic problem and makes the next steps more straightforward.

Equivalent expressions are different ways of writing the same mathematical expression. They may look different but have the same value. For example, the expressions \(5x - 20\) and \(5(x - 4)\) are equivalent because when simplified, they give the same result. Understanding equivalent expressions is crucial because:

• It allows you to recognize different forms of the same problem.
• It shows that mathematical expressions can be simplified or transformed in various ways while retaining their meaning.
• It helps check the correctness of solutions by comparing different forms of the expression.

In our exercise, by factoring out the common factor 5, we transformed the expression \(5x - 20\) into its equivalent form \(5(x - 4)\). This simplified form aids in quickly matching it to the provided options and determining that Option C is correct.

Simplifying expressions involves reducing them to their most basic form. This makes it easier to understand and work with them. The process often includes:

• Identifying and factoring out common factors.
• Combining like terms.
• Using distributive properties to condense or expand expressions as needed.

In the given exercise, we started with \(5x - 20\). By finding the common factor (5) and factoring it out, we simplified the expression to \(5(x - 4)\). Simplifying expressions is a useful skill that helps in solving equations, understanding relationships between variables, and making calculations more manageable. Always look for opportunities to simplify expressions during algebraic manipulations to make problems easier to solve and understand.