Problem 111 Combine like terms. $$ 4 x-7... [FREE SOLUTION]

Chapter 1: Problem 111

Combine like terms. $$ 4 x-7 x $$

Short Answer

Expert verified

-3x

Step by step solution

- Identify the Like Terms

Like terms are terms that have the same variable raised to the same power. In this case, both terms, 4x and -7x, have the variable x raised to the power of 1.

- Combine the Coefficients

To combine like terms, add or subtract their coefficients. The coefficients of 4x and -7x are 4 and -7, respectively. Perform the operation: 4 - 7 = -3

- Rewrite the Expression

After combining the coefficients, replace them with the result while keeping the common variable x. Therefore, 4x - 7x = -3x.

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Key Concepts

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

Coefficients

Coefficients are the numerical parts of terms that include variables. For example, in the term $4x$, the coefficient is 4. Likewise, in $-7x$, the coefficient is -7. Coefficients tell us how many times the variable is being multiplied. In the exercise given, you combine like terms by adding or subtracting these coefficients.To keep track of coefficients:

Locate the numeric part in front of the variable.
Pay attention to the signs (+ or -) before the numbers.

Combining coefficients is straightforward. In the expression $4x - 7x$, you subtract the coefficients because one is positive (4) and the other is negative (-7). Hence, you get $4 - 7 = -3$.So the coefficient of the result, which is $-3x$, simplifies the expression.

Like Terms

Like terms are terms that have the same variables raised to the same powers. This means they can be combined through addition or subtraction. In the provided example, the terms $4x$ and $-7x$ are like terms. Both have the same variable 'x' raised to the power of 1.To identify like terms:

Check that the variables match exactly.
Ensure the exponents on the variables are the same.

Once you've identified like terms, you can combine them by adding or subtracting their coefficients, while keeping the variable part unchanged.For example:

Combine $4x$ and $-7x$
Get $-3x$

This makes the expression much simpler and clearer.

Variables

Variables are symbols used to represent unknown or changeable values. They are usually denoted by letters such as 'x', 'y', or 'z'. In mathematics, variables can play different roles. They can be constants in certain scenarios or changeable in others.In the given exercise, 'x' is the variable present in both terms.To understand variables:

Recognize them as placeholders for numbers.
Know they can be combined when they appear in like terms (with the same exponent).

For example, in $4x$ and $-7x$, 'x' represents the same unknown value in both terms. When you combine these terms, the variable 'x' remains part of the result. Thus, $4x - 7x = -3x$.This approach simplifies the expression while retaining the variable that represents the unknown value.

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91影视

Combine like terms. $$ 4 x-7 x $$

Short Answer

Step by step solution

- Identify the Like Terms

- Combine the Coefficients

- Rewrite the Expression

Key Concepts

Coefficients

Like Terms

Variables

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