Simplify The Expression: 4 X − 5 − 12 X + 3 4x - 5 - 12x + 3 4 X − 5 − 12 X + 3

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Introduction

Simplifying algebraic expressions is a fundamental concept in mathematics, and it plays a crucial role in solving equations and inequalities. In this article, we will focus on simplifying the given expression: $4x - 5 - 12x + 3$. We will use various techniques to simplify the expression and provide a clear understanding of the process.

Understanding the Expression

The given expression is a combination of four terms: $4x$, $-5$, $-12x$, and $3$. To simplify the expression, we need to combine like terms, which are terms that have the same variable raised to the same power.

Combining Like Terms

Like terms are terms that have the same variable raised to the same power. In the given expression, we have two like terms: $4x$ and $-12x$. These terms have the same variable $x$ raised to the same power, which is $1$. To combine these terms, we need to add their coefficients.

Adding Coefficients

The coefficient of a term is the numerical value that is multiplied by the variable. In the case of $4x$, the coefficient is $4$, and in the case of $-12x$, the coefficient is $-12$. To add these coefficients, we need to combine them using the following rule:

• When adding coefficients with the same sign, we add their values.
• When adding coefficients with different signs, we subtract their values.

Using this rule, we can add the coefficients of $4x$ and $-12x$ as follows:

$4 + (-12) = -8$

So, the combined term is $-8x$.

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression by combining the remaining terms. The expression now becomes:

$-8x - 5 + 3$

To simplify this expression, we need to combine the constants. The constants are the numerical values that are not multiplied by any variable. In this case, we have two constants: $-5$ and $3$. To combine these constants, we need to add their values.

Adding Constants

Using the rule mentioned earlier, we can add the constants as follows:

$-5 + 3 = -2$

So, the simplified expression is:

$-8x - 2$

Conclusion

In this article, we simplified the given expression: $4x - 5 - 12x + 3$. We used various techniques to combine like terms and add coefficients. The simplified expression is $-8x - 2$. This expression is a combination of two terms: $-8x$ and $-2$. The term $-8x$ is a linear term, and the term $-2$ is a constant term.

Final Answer

The final answer is $\boxed{-8x - 2}$.

Frequently Asked Questions

Q: What is the simplified expression of $4x - 5 - 12x + 3$?

A: The simplified expression is $-8x - 2$.

Q: How do you combine like terms in an algebraic expression?

A: To combine like terms, you need to add their coefficients. If the coefficients have the same sign, you add their values. If the coefficients have different signs, you subtract their values.

Q: What is the difference between a coefficient and a constant?

A: A coefficient is the numerical value that is multiplied by the variable, while a constant is a numerical value that is not multiplied by any variable.

Q: How do you add constants in an algebraic expression?

A: To add constants, you need to add their values. If the constants have the same sign, you add their values. If the constants have different signs, you subtract their values.

Step-by-Step Solution

Step 1: Identify the like terms in the expression.

The like terms in the expression are $4x$ and $-12x$.

Step 2: Combine the like terms by adding their coefficients.

The coefficient of $4x$ is $4$, and the coefficient of $-12x$ is $-12$. To combine these coefficients, we need to add their values:

$4 + (-12) = -8$

So, the combined term is $-8x$.

Step 3: Simplify the expression by combining the remaining terms.

The expression now becomes:

$-8x - 5 + 3$

To simplify this expression, we need to combine the constants. The constants are the numerical values that are not multiplied by any variable. In this case, we have two constants: $-5$ and $3$. To combine these constants, we need to add their values:

$-5 + 3 = -2$

So, the simplified expression is:

$-8x - 2$

Step 4: Write the final answer.

The final answer is $\boxed{-8x - 2}$.

Additional Resources

For more information on simplifying algebraic expressions, you can refer to the following resources:

• Khan Academy: Simplifying Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Algebra.com: Simplifying Algebraic Expressions

Conclusion

In this article, we simplified the given expression: $4x - 5 - 12x + 3$. We used various techniques to combine like terms and add coefficients. The simplified expression is $-8x - 2$. This expression is a combination of two terms: $-8x$ and $-2$. The term $-8x$ is a linear term, and the term $-2$ is a constant term.

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Introduction

In our previous article, we simplified the given expression: $4x - 5 - 12x + 3$. We used various techniques to combine like terms and add coefficients. In this article, we will provide a Q&A section to help you understand the concept better.

Frequently Asked Questions

Q: What is the simplified expression of $4x - 5 - 12x + 3$?

A: The simplified expression is $-8x - 2$.

Q: How do you combine like terms in an algebraic expression?

A: To combine like terms, you need to add their coefficients. If the coefficients have the same sign, you add their values. If the coefficients have different signs, you subtract their values.

Q: What is the difference between a coefficient and a constant?

A: A coefficient is the numerical value that is multiplied by the variable, while a constant is a numerical value that is not multiplied by any variable.

Q: How do you add constants in an algebraic expression?

A: To add constants, you need to add their values. If the constants have the same sign, you add their values. If the constants have different signs, you subtract their values.

Q: What is the rule for combining like terms?

A: The rule for combining like terms is to add their coefficients. If the coefficients have the same sign, you add their values. If the coefficients have different signs, you subtract their values.

Q: Can you provide an example of combining like terms?

A: Yes, let's consider the expression: $2x + 3x - 4x + 5$. To combine like terms, we need to add their coefficients:

$2 + 3 - 4 = 1$

So, the combined term is $x$. The expression now becomes:

$x + 5$

Q: How do you simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and add coefficients. You also need to combine constants and simplify the expression.

Q: What is the final answer for the expression: $4x - 5 - 12x + 3$?

A: The final answer is $\boxed{-8x - 2}$.

Step-by-Step Solution

Step 1: Identify the like terms in the expression.

The like terms in the expression are $4x$ and $-12x$.

Step 2: Combine the like terms by adding their coefficients.

The coefficient of $4x$ is $4$, and the coefficient of $-12x$ is $-12$. To combine these coefficients, we need to add their values:

$4 + (-12) = -8$

So, the combined term is $-8x$.

Step 3: Simplify the expression by combining the remaining terms.

The expression now becomes:

$-8x - 5 + 3$

To simplify this expression, we need to combine the constants. The constants are the numerical values that are not multiplied by any variable. In this case, we have two constants: $-5$ and $3$. To combine these constants, we need to add their values:

$-5 + 3 = -2$

So, the simplified expression is:

$-8x - 2$

Step 4: Write the final answer.

The final answer is $\boxed{-8x - 2}$.

Additional Resources

For more information on simplifying algebraic expressions, you can refer to the following resources:

• Khan Academy: Simplifying Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Algebra.com: Simplifying Algebraic Expressions

Conclusion

In this article, we provided a Q&A section to help you understand the concept of simplifying algebraic expressions. We answered various questions related to combining like terms, adding coefficients, and simplifying expressions. We also provided a step-by-step solution to simplify the expression: $4x - 5 - 12x + 3$. The final answer is $\boxed{-8x - 2}$.

Final Answer

The final answer is $\boxed{-8x - 2}$.

Related Questions

Q: What is the simplified expression of $2x + 3x - 4x + 5$?

A: The simplified expression is $x + 5$.

Q: How do you combine like terms in the expression: $3x + 2x - 5x + 4$?

A: To combine like terms, you need to add their coefficients. The coefficient of $3x$ is $3$, the coefficient of $2x$ is $2$, and the coefficient of $-5x$ is $-5$. To combine these coefficients, we need to add their values:

$3 + 2 - 5 = 0$

So, the combined term is $0x$ or simply $0$.

Q: What is the final answer for the expression: $3x + 2x - 5x + 4$?

A: The final answer is $\boxed{0 + 4}$ or simply $\boxed{4}$.

Final Thoughts

Simplifying algebraic expressions is an essential concept in mathematics. It helps us to solve equations and inequalities by combining like terms and adding coefficients. In this article, we provided a Q&A section to help you understand the concept better. We also provided a step-by-step solution to simplify the expression: $4x - 5 - 12x + 3$. The final answer is $\boxed{-8x - 2}$.