Problem 3 Simplify each expression by comb... [FREE SOLUTION]

Chapter 1: Problem 3

Simplify each expression by combining any like terms. $$ 8 w-w+6 w $$

Short Answer

Expert verified

The expression simplifies to $13w$.

Step by step solution

Identify Like Terms

In the expression $8w - w + 6w$, identify like terms. Like terms in this expression are terms that have the same variable raised to the same power. Here, all terms ($8w, -w,$ and $6w$) are like terms because they all involve the variable $w$.

Combine Like Terms

Add or subtract the coefficients of the like terms. The coefficients for the terms are 8, -1, and 6. Combine them: $8 - 1 + 6 = 13$. Thus, the combined term becomes $13w$.

Write the Simplified Expression

After combining the like terms, the simplified expression is $13w$.

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Key Concepts

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

Like Terms

In algebra, one often hears about 'like terms.' But what exactly does this mean? Like terms are terms within an algebraic expression that have identical variables raised to the same exponent.
For example, in the expression $8w - w + 6w$, all the terms $8w$, $-w$, and $6w$ are like terms. They all feature the variable $w$ raised to the first power.
Recognizing like terms is crucial because it allows us to simplify expressions by combining them. Whenever you see terms that share the same variable and exponent, you know you have like terms that you can combine.

Coefficients

When dealing with algebraic expressions, you'll frequently encounter the term 'coefficients.' A coefficient refers to the numerical part of a term. It is the number that is directly multiplied by the variable in an algebraic expression.
Let's look at the expression $8w - w + 6w$. Each term here has a coefficient:

For $8w$, the coefficient is 8.
For $-w$, even though the coefficient isn't explicitly stated, it is $-1$.
Finally, the coefficient for $6w$ is 6.

Understanding coefficients is essential because they are what you add or subtract when you combine like terms. They tell you how many of each term you have, which is key to simplifying the expression.

Combining Like Terms

After identifying like terms and recognizing their coefficients, the next step is combining them to simplify the expression. This process involves adding or subtracting the coefficients while keeping the variable part constant.
In the expression $8w - w + 6w$, we identified that all terms are like terms. Now, focus on their coefficients: $8$, $-1$, and $6$.
We combine these coefficients like this:

Add $8$ and $6$ to get $14$.
Subtract $1$ from $14$ to get $13$.

Thus, the like terms combine to form one simplified term: $13w$. This step is essential in reducing expressions to their simplest form, making equations easier to solve and understand.

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91影视

Simplify each expression by combining any like terms. $$ 8 w-w+6 w $$

Short Answer

Step by step solution

Identify Like Terms

Combine Like Terms

Write the Simplified Expression

Key Concepts

Like Terms

Coefficients

Combining Like Terms

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