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Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblema 20
Capitolo 1, Problema 20

Simplify the algebraic expression. (1/5)(5x) + [(3y) + (- 3y)] - (-x)

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Distribute the fraction \( \frac{1}{5} \) to \( 5x \). This means multiplying \( \frac{1}{5} \times 5x \), which simplifies to \( x \).
Simplify the expression inside the brackets \( (3y) + (-3y) \). Since \( 3y - 3y = 0 \), the entire bracket simplifies to \( 0 \).
Handle the subtraction of \( -x \). Subtracting \( -x \) is equivalent to adding \( x \), so \( -(-x) = x \).
Combine all simplified terms: \( x + 0 + x \).
Add the like terms \( x + x \) to further simplify the expression.

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Distributive Property

The Distributive Property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term within a set of parentheses, which is essential for simplifying expressions. In the given expression, applying this property helps in distributing the coefficient (1/5) to the term (5x).
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Multiply Polynomials Using the Distributive Property

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. In the expression, (3y) and (-3y) are like terms that cancel each other out, simplifying the expression significantly. This concept is crucial for reducing expressions to their simplest form.
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Combinations

Negative Signs and Their Effects

Understanding negative signs is vital in algebra, as they can change the value of terms. In the expression, the term -(-x) simplifies to +x, demonstrating how two negative signs result in a positive. This concept is important for correctly interpreting and simplifying expressions involving negative values.
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Zero and Negative Rules
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