Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problem 93

Chapter 1, Problem 93

In Exercises 85–96, simplify each algebraic expression. 7−4[3−(4y−5)]

Verified step by step guidance

Start by simplifying the innermost parentheses: (4y - 5). Since there are no operations to perform inside, leave it as is.

Next, simplify the expression inside the brackets: 3 - (4y - 5). Distribute the negative sign across (4y - 5), resulting in 3 - 4y + 5.

Combine like terms within the brackets: 3 + 5 becomes 8, so the expression inside the brackets becomes 8 - 4y.

Now substitute the simplified expression back into the original equation: 7 - 4[8 - 4y].

Distribute the -4 across the terms inside the brackets: -4 * 8 = -32 and -4 * -4y = 16y. This results in 7 - 32 + 16y. Combine like terms to simplify further.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In the given expression, operations within parentheses must be addressed first, followed by multiplication and then addition or subtraction.

Distributive Property

The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term within a set of parentheses. This property is essential for simplifying expressions that involve multiplication of a term with a sum or difference. In the expression provided, applying the distributive property will help simplify the term -4[3 - (4y - 5)] effectively.

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. This process is crucial for reducing expressions to their simplest form. After applying the order of operations and the distributive property in the given expression, combining like terms will help finalize the simplification.

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