Simplify The Expression: 4 X − 7 Y − 5 Z + 6 4x - 7y - 5z + 6 4 X − 7 Y − 5 Z + 6

$$

Introduction

In mathematics, simplifying expressions is an essential skill that helps us to solve problems more efficiently and accurately. It involves combining like terms and eliminating any unnecessary components from the expression. In this article, we will focus on simplifying the given expression: $4x - 7y - 5z + 6$. We will break down the steps involved in simplifying the expression and provide a clear explanation of each step.

Understanding the Expression

The given expression is a linear combination of three variables: $x$, $y$, and $z$. It consists of four terms: $4x$, $-7y$, $-5z$, and $6$. To simplify the expression, we need to combine like terms and eliminate any unnecessary components.

Combining Like Terms

Like terms are terms that have the same variable raised to the same power. In this expression, we have three like terms: $4x$, $-7y$, and $-5z$. We can combine these terms by adding or subtracting their coefficients.

Step 1: Combine the Coefficients of $x$

The coefficient of $x$ is $4$. Since there are no other terms with $x$, we can leave the coefficient as it is.

Step 2: Combine the Coefficients of $y$

The coefficient of $y$ is $-7$. Since there are no other terms with $y$, we can leave the coefficient as it is.

Step 3: Combine the Coefficients of $z$

The coefficient of $z$ is $-5$. Since there are no other terms with $z$, we can leave the coefficient as it is.

Step 4: Combine the Constant Terms

The constant term is $6$. Since there are no other constant terms, we can leave the constant term as it is.

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression by adding or subtracting the coefficients.

$4x - 7y - 5z + 6$

Since there are no like terms to combine, the expression is already simplified.

Conclusion

In this article, we simplified the expression $4x - 7y - 5z + 6$ by combining like terms and eliminating any unnecessary components. We broke down the steps involved in simplifying the expression and provided a clear explanation of each step. By following these steps, we can simplify any linear expression and solve problems more efficiently and accurately.

Frequently Asked Questions

• What is the simplified form of the expression $4x - 7y - 5z + 6$?
• How do we combine like terms in an expression?
• What are the steps involved in simplifying a linear expression?

Answer

• The simplified form of the expression $4x - 7y - 5z + 6$ is $4x - 7y - 5z + 6$.
• To combine like terms, we add or subtract the coefficients of the like terms.
• The steps involved in simplifying a linear expression are:
  1. Identify the like terms in the expression.
  2. Combine the coefficients of the like terms.
  3. Simplify the expression by adding or subtracting the coefficients.

Final Answer

The final answer is $4x - 7y - 5z + 6$.

$$

Introduction

In our previous article, we simplified the expression $4x - 7y - 5z + 6$ by combining like terms and eliminating any unnecessary components. In this article, we will provide a Q&A section to help you understand the concept of simplifying expressions better.

Q&A

Q1: What is the simplified form of the expression $4x - 7y - 5z + 6$?

A1: The simplified form of the expression $4x - 7y - 5z + 6$ is $4x - 7y - 5z + 6$.

Q2: How do we combine like terms in an expression?

A2: To combine like terms, we add or subtract the coefficients of the like terms.

Q3: What are the steps involved in simplifying a linear expression?

A3: The steps involved in simplifying a linear expression are:

1. Identify the like terms in the expression.
2. Combine the coefficients of the like terms.
3. Simplify the expression by adding or subtracting the coefficients.

Q4: Can we simplify an expression with more than one variable?

A4: Yes, we can simplify an expression with more than one variable by combining like terms and eliminating any unnecessary components.

Q5: How do we identify like terms in an expression?

A5: To identify like terms, we look for terms that have the same variable raised to the same power.

Q6: Can we simplify an expression with a constant term?

A6: Yes, we can simplify an expression with a constant term by combining the constant terms and eliminating any unnecessary components.

Q7: What is the difference between combining like terms and simplifying an expression?

A7: Combining like terms involves adding or subtracting the coefficients of the like terms, while simplifying an expression involves eliminating any unnecessary components and combining like terms.

Q8: Can we simplify an expression with a negative coefficient?

A8: Yes, we can simplify an expression with a negative coefficient by combining the coefficients and eliminating any unnecessary components.

Q9: How do we simplify an expression with a fraction?

A9: To simplify an expression with a fraction, we can multiply the numerator and denominator by the same value to eliminate the fraction.

Q10: Can we simplify an expression with a variable in the denominator?

A10: Yes, we can simplify an expression with a variable in the denominator by multiplying the numerator and denominator by the same value to eliminate the variable in the denominator.

Conclusion

In this Q&A article, we provided answers to common questions related to simplifying expressions. We hope that this article has helped you understand the concept of simplifying expressions better.

Frequently Asked Questions

• What is the simplified form of the expression $4x - 7y - 5z + 6$?
• How do we combine like terms in an expression?
• What are the steps involved in simplifying a linear expression?

Answer

• The simplified form of the expression $4x - 7y - 5z + 6$ is $4x - 7y - 5z + 6$.
• To combine like terms, we add or subtract the coefficients of the like terms.
• The steps involved in simplifying a linear expression are:
  1. Identify the like terms in the expression.
  2. Combine the coefficients of the like terms.
  3. Simplify the expression by adding or subtracting the coefficients.

Final Answer

The final answer is $4x - 7y - 5z + 6$.