Problem 34 $$ \begin{array}{r} 9 x+7 \\... [FREE SOLUTION]

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Elementary Algebra Within Reach

Ron Larson, Kimberly Nolting

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 5: Problem 34

$$ \begin{array}{r} 9 x+7 \\ -(3 x+9) \\ \hline \end{array} $$

Short Answer

Expert verified

The answer to the problem is $6x - 2$.

Step by step solution

Subtract the variables

Subtract the variables, one from the other. That is, subtract $3x$ from $9x$, getting $6x$ as the result.

Subtract the constants

Now, subtract the constants, one from the other. $7 - 9$ yields $-2$.

Combine the results

Now, combine the results of steps 1 and 2 to form the final equation. This gives us $6x - 2$.

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Key Concepts

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

Subtracting Polynomials

Subtracting polynomials involves finding the difference between two polynomial expressions term by term. Each term consists of variables (like $ x $) and constants (like 7 or -2). When subtracting, we remember to distribute the negative sign across the terms being subtracted.

For example, in the given exercise, $9x+7-(3x+9)$, we distribute the negative sign to $3x$ and $+9$, changing the equation to $9x+7-3x-9$. We then proceed to subtract the terms with variables from each other and the constants from one another. This stepwise approach makes the subtraction clear and avoids common mistakes.

Combining Like Terms

Combining like terms is an essential strategy in simplifying algebraic expressions. Like terms are terms that have the exact same variables raised to the same power. They can be combined by adding or subtracting their coefficients.

In our exercise, $9x$ and $3x$ are like terms. We subtract them as shown in step 1 of the solution to yield $6x$. No like terms remain after this, as $7$ and $9$ are constants. This process simplifies the expression to $6x - 2$, making it easier to understand and use in further calculations.

Algebraic Operations

Algebraic operations include addition, subtraction, multiplication, and division, which can be applied to algebraic expressions. When dealing with subtraction, as in the exercise, it's crucial to pay attention to the signs of each term.

Applying the subtraction operation carefully helps us avoid sign errors that can completely change the result. The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), should be followed to ensure accuracy.

Elementary Algebra

Elementary Algebra forms the foundation of more advanced branches of mathematics. It introduces us to concepts, operations, and techniques that are fundamental to understanding and solving equations.

The exercise we solved embodies elementary algebra where we deal with variables, coefficients, and simple algebraic manipulations to simplify expressions. Mastering subtraction of polynomials and combining like terms is crucial in algebra since these skills are frequently applied to a wide variety of problems, from simple equations to complex functions.

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91影视

$$ \begin{array}{r} 9 x+7 \\ -(3 x+9) \\ \hline \end{array} $$

Short Answer

Step by step solution

Subtract the variables

Subtract the constants

Combine the results

Key Concepts

Subtracting Polynomials

Combining Like Terms

Algebraic Operations

Elementary Algebra

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