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Chapter 11: Problem 57

Collect like terms. $$ 11 x-3 x $$

Short Answer

Expert verified
The simplified expression is 8x.

Step by step solution

01

Identify like terms

Look at the terms given: 11x and -3x. Both of these terms have the variable x and are therefore like terms.
02

Combine the coefficients

Add the coefficients of the like terms 11 and -3. This means calculating 11 - 3.
03

Write the simplified expression

The result of 11 - 3 is 8. Therefore, combining the like terms gives the simplified expression 8x.

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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 essential to recognize 'like terms'. Like terms are terms that have the same variable raised to the same power. In the example given, 11x and -3x are both like terms because they share the same variable 'x'. This is crucial for further simplification. If one term had been, say, 11x and the other was 3y, they wouldn't be like terms. We can only combine terms that are 'like', which means they share the same variable component.
combining coefficients
Once we have identified the like terms, the next step is 'combining coefficients'. The coefficient is the numerical part of the term that multiplies the variable. In the given problem, the coefficients are 11 and -3. To combine them, we perform the operation indicated, which, in this case, is subtraction since we have 11 - 3. Remember, if both coefficients were positive, you would add them, and if one or both are negative, you add or subtract according to standard arithmetic rules.
simplified expression
After combining the coefficients of the like terms, we achieve a 'simplified expression'. Here's how it works in our problem: combining 11 and -3 gives us 8. So, the terms 11x and -3x combine to become 8x. This is our simplified expression. The goal of simplification is to make an expression easier to work with by consolidating like terms and reducing the overall complexity, making future calculations more manageable.

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