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Chapter 1: Problem 805

Simplify using the distributive property. $$ 22-(a+3) $$

Short Answer

Expert verified
19-a

Step by step solution

01

Identify the terms

The original expression is \(22-(a+3)\). It consists of a constant term, 22, and a term inside the parentheses, \(a+3\).
02

Apply the distributive property

Using the distributive property, distribute the negative sign to both terms inside the parentheses: \(22 - (a + 3) = 22 - a - 3\).
03

Combine like terms

Combine the constants: \(22 - 3 - a\). Simplifying this gives \(19 - a\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Expressions
Simplifying expressions is a fundamental skill in algebra. It involves breaking down complex expressions into simpler ones. This can make it easier to understand and solve problems.
For example, when simplifying the expression \(22 - (a + 3)\), you start by removing the parentheses. This is often achieved using the distributive property.
Simplifying expressions helps reduce errors and makes calculations manageable.
Practice simplifying different expressions to strengthen your understanding.
Combining Like Terms
Combining like terms is another key aspect of algebra. Like terms are terms with the same variable raised to the same power. For instance, in the expression \(22 - (a + 3)\), the terms \(22\) and \(3\) are constants and can be combined.
Removing the parentheses, we get \(22 - a - 3\). Here, \(22\) and \(3\) are like terms and can be combined to simplify the expression to \(19 - a\).
Remember, only terms with the same variable and exponent can be combined. This simplifies the expression and helps solve equations more easily.
Algebraic Operations
Algebraic operations include addition, subtraction, multiplication, and division applied to algebraic expressions. These operations follow specific rules.
In the given exercise, we applied the distributive property鈥攁 key algebraic operation. The distributive property helps in breaking down expressions involving parentheses: \(a(b + c) = ab + ac\).
For instance, in the expression \(22 - (a + 3)\), we distributed the negative sign: \(22 - (a + 3) = 22 - a - 3\).
Practicing algebraic operations like this strengthens problem-solving skills and builds confidence in handling more complex equations.

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