Problem 52 Simplify it by combining any lik... [FREE SOLUTION]

Chapter 5: Problem 52

Simplify it by combining any like terms. $$ -x-4.1-x-4.02 $$

Short Answer

Expert verified

The simplified expression is $-2x - 8.12$.

Step by step solution

Identify like terms

In the expression $-x - 4.1 - x - 4.02$, the like terms can be identified. The terms $-x$ and $-x$ are like terms because they both contain the variable $x$, while $-4.1$ and $-4.02$ are like terms because they are both constants.

Combine the variable terms

Add the like terms with the variable $x$: $-x - x = -2x$.

Combine the constant terms

Add the constant like terms: $-4.1 - 4.02 = -8.12$.

Write the simplified expression

After combining like terms, the simplified expression is $-2x - 8.12$.

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Key Concepts

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

Understanding Like Terms

In algebra, like terms are terms that contain the same variables raised to the same power. Recognizing like terms is the first step toward simplifying algebraic expressions. For instance, if we have an expression like $-x - 4.1 - x - 4.02$, we need to identify which terms are like terms. Here, both $-x$ terms are classified as like terms because they contain the variable $x$ raised to the same power. On the other hand, the numbers $-4.1$ and $-4.02$ are like terms because they are both constants.

Recognizing like terms means looking for similarities:

Terms with identical variables and exponents are like terms.
Constants are naturally like terms with each other since they lack variables.

Ignoring like terms leads to mistakes in simplification, so this skill is crucial.

Combining Like Terms

Once you have identified like terms, the next step in simplifying an algebraic expression is combining them. This means adding or subtracting the coefficients of these terms. Consider our expression: $-x - 4.1 - x - 4.02$.

First, we combine the $-x$ terms. Since both are $-x$, we add their coefficients, which are both $-1$. Hence, $-1 - 1 = -2$, and their sum is $-2x$. Similarly, we combine the constant terms $-4.1$ and $-4.02$ to get $-8.12$.

To correctly combine like terms, remember:

Add the coefficients when like terms have addition or equal to the operation.
Subtract for subtraction operations.

The expression becomes easier to handle once like terms are combined, paving the way for further simplification.

Algebraic Simplification

The goal of algebraic simplification is to condense expressions into their simplest, most compact form by eliminating redundancies. After identifying and combining like terms, as we did with our $-x - 4.1 - x - 4.02$ expression, this results in $-2x - 8.12$. Simplification not only makes expressions easier to understand but also facilitates solving equations or further algebraic manipulation.

Remember these steps for algebraic simplification:

Identify like terms: find terms that share the same variables and exponents.
Combine these terms systematically to consolidate them.
Check for any errors, ensuring you have simplified as much as possible.

Not all expressions involve further steps beyond combining like terms, but ensuring you reach the simplest form is always essential.

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91影视

Simplify it by combining any like terms. $$ -x-4.1-x-4.02 $$

Short Answer

Step by step solution

Identify like terms

Combine the variable terms

Combine the constant terms

Write the simplified expression

Key Concepts

Understanding Like Terms

Combining Like Terms

Algebraic Simplification

One App. One Place for Learning.

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