Problem 39 Simplify each expression. $$ ... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 1: Problem 39

Simplify each expression. $$ -6 x-3 x $$

Short Answer

Expert verified

-9x

Step by step solution

Identify like terms

The given expression is $-6x - 3x$. Notice that both terms have the variable $x$. These are like terms and can be combined.

Combine like terms

Add the coefficients of $x$. The coefficients are $-6$ and $-3$. Combine them by adding: $-6 + (-3)$.

Simplify the coefficients

Simplify the addition of the coefficients: $-6 + (-3) = -9$.

Combine with the variable

Multiply the simplified coefficient with the variable $x$. The final expression is $-9x$.

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Key Concepts

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

like terms

When simplifying algebraic expressions, it's important to identify 'like terms'. Like terms are terms that contain the same variable(s) raised to the same power. For instance, in the expression $-6x - 3x$, both terms have the variable $x$. This means they are like terms. If the terms do not have identical variables and exponents, they cannot be combined. This is an essential first step in the simplification process.

combining coefficients

Once you have identified like terms, the next step is 'combining coefficients' of these terms. In our example, the coefficients are $-6$ and $-3$. To combine them, add the coefficients together: $-6 + (-3)$. It's important to keep the sign of the numbers in mind. In this case, the result is $-9$. By combining coefficients, you are making the expression simpler and easier to work with.

algebraic simplification

The goal of algebraic simplification is to rewrite an expression in its simplest form. After we've combined like terms and their coefficients, we need to simplify the result further if possible. In the given problem, after combining $-6x - 3x$ to get $-9x$, there are no further steps needed because $-9x$ is already in its simplest form. Simplifying algebraic expressions makes solving equations more straightforward and reduces the complexity of the problems.

variable terms

Variable terms consist of a number (coefficient) multiplied by a variable. For example, in $-6x - 3x$, \-6x\ and \-3x\ are variable terms. The variable, in this case, is $'x'$. When dealing with variable terms, it鈥檚 crucial to handle them appropriately during the simplification process. Remember, terms with different variables or exponents cannot be combined. This is because they represent different quantities or entities. Correctly processing variable terms allows you to achieve accurate simplification of algebraic expressions.

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91影视

Simplify each expression. $$ -6 x-3 x $$

Short Answer

Step by step solution

Identify like terms

Combine like terms

Simplify the coefficients

Combine with the variable

Key Concepts

like terms

combining coefficients

algebraic simplification

variable terms

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