Evaluate The Expression When $x = 5$ And $y = -4$:$x - 9y$

Introduction

Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill for students and professionals alike. In this article, we will focus on evaluating the expression $x - 9y$ when $x = 5$ and $y = -4$. We will break down the problem step by step, using simple language and clear explanations to ensure that readers understand the process.

Understanding the Expression

The given expression is $x - 9y$. This is a linear expression, which means it is a polynomial of degree one. The expression consists of two terms: $x$ and $-9y$. The first term is a variable $x$, and the second term is a product of a constant $-9$ and a variable $y$.

Substituting the Values of $x$ and $y$

To evaluate the expression, we need to substitute the values of $x$ and $y$ into the expression. We are given that $x = 5$ and $y = -4$. We will replace the variables in the expression with these values.

Evaluating the Expression

Now that we have substituted the values of $x$ and $y$, we can evaluate the expression. We will start by evaluating the first term, which is $x$. Since $x = 5$, we can substitute this value into the expression:

$x - 9y = 5 - 9y$

Next, we will evaluate the second term, which is $-9y$. Since $y = -4$, we can substitute this value into the expression:

$5 - 9y = 5 - 9(-4)$

Simplifying the Expression

Now that we have evaluated both terms, we can simplify the expression. We will start by evaluating the product $-9(-4)$. This is a negative times a negative, which is equal to a positive:

$-9(-4) = 36$

Now that we have evaluated the product, we can substitute this value back into the expression:

$5 - 9y = 5 + 36$

Final Answer

Now that we have simplified the expression, we can find the final answer. We will start by combining the constants in the expression:

$5 + 36 = 41$

Therefore, the final answer is:

$x - 9y = 41$

Conclusion

Evaluating algebraic expressions is a crucial skill for students and professionals alike. In this article, we have walked through the process of evaluating the expression $x - 9y$ when $x = 5$ and $y = -4$. We have broken down the problem step by step, using simple language and clear explanations to ensure that readers understand the process. By following these steps, readers can evaluate algebraic expressions with confidence.

Frequently Asked Questions

• Q: What is an algebraic expression? A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations.
• Q: How do I evaluate an algebraic expression? A: To evaluate an algebraic expression, you need to substitute the values of the variables into the expression and then simplify the expression using the order of operations.
• Q: What is the order of operations? A: The order of operations is a set of rules that tells you which operations to perform first when evaluating an expression. The order of operations is: parentheses, exponents, multiplication and division, and addition and subtraction.

Additional Resources

• Khan Academy: Algebra
• Mathway: Algebra Calculator
• Wolfram Alpha: Algebra Solver

Related Articles

• Evaluating Algebraic Expressions with Variables
• Solving Linear Equations with Variables
• Graphing Linear Equations with Variables
  

Introduction

Evaluating algebraic expressions is a crucial skill for students and professionals alike. In our previous article, we walked through the process of evaluating the expression $x - 9y$ when $x = 5$ and $y = -4$. In this article, we will answer some of the most frequently asked questions about evaluating algebraic expressions.

Q&A

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. Algebraic expressions can be simple, such as $x + 3$, or complex, such as $2x^2 + 5x - 3$.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the values of the variables into the expression and then simplify the expression using the order of operations. The order of operations is: parentheses, exponents, multiplication and division, and addition and subtraction.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when evaluating an expression. The order of operations is:

1. Parentheses: Evaluate any expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., $x^2$).
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, $2x$ and $3x$ are like terms, but $2x$ and $3y$ are not.

Q: What is a variable?

A: A variable is a letter or symbol that represents a value that can change. Variables are used to represent unknown values in algebraic expressions.

Q: What is a constant?

A: A constant is a value that does not change. Constants are used to represent fixed values in algebraic expressions.

Q: How do I evaluate an expression with multiple variables?

A: To evaluate an expression with multiple variables, you need to substitute the values of all the variables into the expression and then simplify the expression using the order of operations.

Q: What is the difference between an equation and an expression?

A: An equation is a statement that says two expressions are equal. An expression is a mathematical statement that contains variables, constants, and mathematical operations.

Q: How do I solve an equation with variables?

A: To solve an equation with variables, you need to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Conclusion

Evaluating algebraic expressions is a crucial skill for students and professionals alike. In this article, we have answered some of the most frequently asked questions about evaluating algebraic expressions. By following the steps outlined in this article, you can evaluate algebraic expressions with confidence.

Frequently Asked Questions

• Q: What is the difference between an equation and an expression? A: An equation is a statement that says two expressions are equal. An expression is a mathematical statement that contains variables, constants, and mathematical operations.
• Q: How do I simplify an algebraic expression? A: To simplify an algebraic expression, you need to combine like terms.
• Q: What is a variable? A: A variable is a letter or symbol that represents a value that can change.
• Q: What is a constant? A: A constant is a value that does not change.

Additional Resources

• Khan Academy: Algebra
• Mathway: Algebra Calculator
• Wolfram Alpha: Algebra Solver

Related Articles

• Evaluating Algebraic Expressions with Variables
• Solving Linear Equations with Variables
• Graphing Linear Equations with Variables