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Chapter 1: Problem 34

Simplify each algebraic expression by combining similar terms. $$-6 m-m+17 m$$

Short Answer

Expert verified
10m

Step by step solution

01

Identify Like Terms

In the expression \(-6m - m + 17m\), the terms are \(-6m\), \(-m\), and \(17m\). All these terms involve the variable \(m\), so they are like terms and can be combined.
02

Combine Like Terms

Add the coefficients of the terms: \(-6\), \(-1\), and \(17\). Calculate the result: \(-6 - 1 + 17 = 10\).
03

Write the Simplified Expression

After combining the coefficients, the simplified expression is \(10m\).

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Key Concepts

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

Combining Like Terms
When you're working with algebraic expressions, one of the first steps is to simplify them by combining like terms. Like terms are terms that have the exact same variables raised to the same power. In our case, in the expression \[-6m - m + 17m\],all the terms involve the variable \(m\). This means they can be combined because they all contain the same variable component.Here's how you combine:
  • Identify all the terms with the same variables. These are your like terms.
  • Add or subtract their coefficients (the numerical parts) while keeping the variable the same.
For our expression, the process involves looking at the coefficients: \(-6\), \(-1\), and \(17\). When you combine them you get \(-6 - 1 + 17 = 10\). Thus, simply combining these results in a more concise expression.
Simplifying Expressions
Simplifying expressions is a crucial skill in algebra because it allows for easier manipulation and understanding of equations. The goal is to reduce the expression to its simplest form while maintaining its equality. To achieve this:
  • Combine any like terms as indicated in the previous section.
  • Order the terms, usually from the highest degree to the lowest, if applicable.
In this problem, after combining the like terms, the expression simplifies to \(10m\). This is because all terms have been consolidated into a single, easily readable expression. Simplification is valuable because it provides a clear and concise form that's easy to interpret and further manipulate if needed.
Algebraic Coefficients
In any algebraic expression, coefficients are the numerical parts that multiply the variables. They play a key role in defining the quantity of the variable. Recognizing and understanding coefficients is important when simplifying expressions.In the expression \[-6m - m + 17m\], you have coefficients such as \(-6\), \(-1\), and \(17\). Some key aspects to remember about coefficients include:
  • They can be positive or negative, which affects addition or subtraction when combining terms.
  • A coefficient of \(1\) or \(-1\) means the variable is simply \(x\) or \(-x\).
Here, the sum of \(-6\), \(-1\), and \(17\) is therefore necessary to simplify the expression effectively to \(10m\). Understanding how these coefficients interact with each other allows you to efficiently perform operations in algebra.

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Most popular questions from this chapter

State the property that justifies each statement. For example, \(3+(-4)=(-4)+3\) because of the commutative property for addition. $$(-9)(17)=17(-9)$$

State in your own words the associative property for addition of integers.

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$-72+[72+(-14)]$$

Find the value of \(\frac{h\left(b_{1}+b_{2}\right)}{2}\) for each set of values for the variables \(h, b_{1}\), and \(b_{2}\). (Subscripts are used to indicate that \(b_{1}\) and \(b_{2}\) are different variables.) \(h=14, b_{1}=9\), and \(b_{2}=7\)

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \((x+12)-(x-14)\) for \(x=-11\)
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