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Chapter 1: Problem 5

Simplify each expression. $$ 4 r+19-8 $$

Short Answer

Expert verified
4r + 11

Step by step solution

01

Identify like terms

In the given expression \(4r + 19 - 8\), identify the like terms. Constants 19 and -8 are like terms.
02

Combine like terms

Add or subtract the constants: \( 19 - 8 = 11 \). So, the expression becomes \( 4r + 11 \).
03

Write the simplified expression

After combining the like terms, the simplified expression is \( 4r + 11 \).

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Key Concepts

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

Like Terms
Like terms are terms in an algebraic expression that have the same variables raised to the same power. This makes them compatible for addition or subtraction. Identifying like terms is crucial in simplifying expressions. For instance, in the expression \( 4r + 19 - 8 \), we can recognize that 19 and -8 are like terms because they are both constants. They do not contain any variables. In contrast, \( 4r \) is a different type of term because it includes the variable \( r \).
Combining Like Terms
Combining like terms involves adding or subtracting them to streamline the expression. Think of it like grouping together similar items. In the expression \( 4r + 19 - 8 \), once we've identified that 19 and -8 are like terms, we need to combine them. Performing the operation, we calculate: $$ 19 - 8 = 11 $$. This simplifies our original expression to \( 4r + 11 \). You simply retain the variable terms as is unless there are other like terms with variables to combine.
Algebraic Simplification
Algebraic simplification means reducing an expression to its simplest form. It involves combining like terms and performing arithmetic operations within the expression. The goal is to make the expression as concise as possible. For the initial expression \( 4r + 19 - 8 \), we've already combined the constants to get \( 4r + 11 \). This method ensures the expression is easier to work with for further mathematical operations, such as solving equations or graphing. Simplification helps to clearly understand the parts of the expression and removes any unnecessary complexity.

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Most popular questions from this chapter

Simplify each expression. $$ -4(-3 x+3)-(6 x-4)-2 x+1 $$

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Write a numerical expression for each phrase and simplify. See Examples 8 and \(9 .\) The difference between 7 and \(-14\)

Simplify each expression. $$ 1+7 x+11 x-1+5 x $$
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