Evaluate 8x + 9 When X = 5 A Step-by-Step Guide
What is the value of the expression 8x + 9 when x equals 5?
In mathematics, evaluating expressions is a fundamental skill. It involves substituting a given value for a variable and then performing the indicated operations. This article will explore the process of evaluating the algebraic expression 8x + 9 when x is equal to 5. We will break down each step, ensuring a clear understanding of the order of operations and the arithmetic involved. This is a crucial concept in algebra and serves as a building block for more complex mathematical problems. Understanding how to correctly substitute and simplify expressions is essential for success in higher-level math courses and various real-world applications.
Understanding the Expression
The algebraic expression 8x + 9 consists of two terms: 8x and 9. The term 8x represents the product of 8 and the variable x. In algebra, a variable is a symbol (usually a letter) that represents a number. The coefficient 8 indicates that the variable x is multiplied by 8. The term 9 is a constant, meaning its value does not change. The plus sign (+) indicates that we need to add the two terms together. To evaluate this expression, we need to substitute the given value of x (which is 5 in this case) into the expression and then perform the necessary arithmetic operations. It's important to remember the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), to ensure we arrive at the correct answer. In this specific expression, we will first perform the multiplication and then the addition. Understanding these basic components of algebraic expressions is essential for tackling more complex problems in algebra and beyond.
Substituting the Value of x
The first step in evaluating the expression 8x + 9 when x = 5 is to substitute the value of x into the expression. This means replacing the variable x with the number 5. When we do this, the expression becomes 8(5) + 9. Notice that we've replaced the x with 5 and used parentheses to clearly indicate that the 8 is being multiplied by 5. This is a crucial step, as it sets the stage for the arithmetic operations we need to perform. Accurate substitution is the foundation of evaluating any algebraic expression. If the substitution is done incorrectly, the subsequent calculations will also be incorrect, leading to a wrong answer. Therefore, it is always important to double-check that the substitution is done correctly before proceeding to the next step. Once the substitution is complete, we can move on to simplifying the expression using the order of operations.
Applying the Order of Operations
Now that we have substituted the value of x, our expression is 8(5) + 9. According to the order of operations (PEMDAS), we must perform multiplication before addition. In this expression, the multiplication operation is 8(5), which means 8 multiplied by 5. Performing this multiplication gives us 40. So, the expression now becomes 40 + 9. The next step is to perform the addition. We add 40 and 9 together. The addition operation is the final step in simplifying this expression. By following the order of operations, we ensure that we are performing the calculations in the correct sequence, which is crucial for arriving at the correct answer. Understanding and applying the order of operations is a fundamental skill in mathematics and is essential for simplifying more complex expressions and equations.
Performing the Arithmetic
After applying the order of operations, we are left with the simple addition problem: 40 + 9. Adding 40 and 9 together gives us 49. This is the final step in evaluating the expression 8x + 9 when x = 5. The arithmetic operation here is straightforward, but it's crucial to perform it accurately to arrive at the correct solution. A small mistake in addition can lead to a completely different answer. Therefore, it's always a good practice to double-check the arithmetic, especially in more complex problems. Once we have performed the addition and obtained the final result, we can confidently say that we have successfully evaluated the expression for the given value of the variable. The result, 49, represents the value of the expression 8x + 9 when x is equal to 5. This process highlights the importance of both algebraic substitution and arithmetic accuracy in mathematics.
The Final Result
After substituting x = 5 into the expression 8x + 9 and performing the necessary arithmetic operations, we arrive at the final result: 49. This means that when x is equal to 5, the value of the expression 8x + 9 is 49. This process of evaluating expressions is a fundamental skill in algebra and is used extensively in various mathematical contexts. The ability to accurately substitute values for variables and simplify expressions is essential for solving equations, graphing functions, and tackling more advanced mathematical concepts. The result, 49, represents a single numerical value that is the outcome of all the operations performed on the substituted value. This single value provides a clear and concise answer to the problem of evaluating the expression for the given value of x. Understanding how to arrive at this result is crucial for developing a strong foundation in algebra and problem-solving in mathematics.
Conclusion
In conclusion, evaluating the expression 8x + 9 when x = 5 involves a straightforward process of substitution and simplification. We first substituted the value of x into the expression, resulting in 8(5) + 9. Then, following the order of operations, we performed the multiplication 8(5) = 40 and subsequently added 9 to the result, yielding 40 + 9 = 49. Therefore, the value of the expression 8x + 9 when x = 5 is 49. This exercise highlights the importance of understanding algebraic expressions, substitution, and the order of operations. These concepts are fundamental to algebra and are essential for solving more complex mathematical problems. Mastering these skills will provide a solid foundation for further studies in mathematics and related fields. The ability to accurately evaluate expressions is not only a valuable mathematical skill but also a crucial tool for problem-solving in various real-world applications. Understanding these basic steps ensures that you can confidently tackle similar problems and build a strong foundation in algebra.
Frequently Asked Questions (FAQ)
1. What is an algebraic expression?
An algebraic expression is a combination of variables, constants, and arithmetic operations (such as addition, subtraction, multiplication, and division). For example, 8x + 9 is an algebraic expression where x is a variable, 8 and 9 are constants, and the operations are multiplication and addition. Algebraic expressions are used to represent mathematical relationships and can be evaluated by substituting specific values for the variables.
2. What does it mean to evaluate an expression?
To evaluate an expression means to find its numerical value by substituting given values for the variables and performing the indicated operations. For instance, when we evaluate 8x + 9 for x = 5, we replace x with 5 and calculate the result. Evaluating expressions is a fundamental skill in algebra and is used to solve equations, simplify formulas, and analyze mathematical relationships.
3. What is the order of operations?
The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed. It is commonly remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Following the order of operations ensures that expressions are evaluated consistently and correctly. In the expression 8x + 9, we first perform the multiplication (8 * 5) and then the addition (40 + 9).
4. Why is it important to follow the order of operations?
Following the order of operations is crucial because it ensures that everyone arrives at the same correct answer when evaluating an expression. Without a standardized order, the same expression could be interpreted and calculated in multiple ways, leading to different results. The order of operations provides a universal rule for simplifying mathematical expressions, which is essential for consistency and accuracy in mathematics and related fields.
5. What is a variable in an algebraic expression?
A variable is a symbol, usually a letter (such as x, y, or z), that represents a quantity that can change or vary. In the expression 8x + 9, x is the variable. The value of a variable is not fixed and can be replaced by different numbers. Variables are used to represent unknown quantities or values that can change within a given context. Understanding variables is fundamental to algebra and is essential for solving equations and modeling real-world situations.
6. How do I substitute a value for a variable?
To substitute a value for a variable, you replace the variable with the given numerical value. For example, to substitute x = 5 into the expression 8x + 9, you replace x with 5, resulting in 8(5) + 9. It's important to use parentheses to indicate multiplication when a number is placed next to a variable or another number. Accurate substitution is crucial for correctly evaluating expressions and solving equations.
7. What happens if I don't follow the order of operations?
If you do not follow the order of operations, you are likely to arrive at an incorrect answer. The order of operations ensures that mathematical expressions are simplified consistently. For example, if you were to add 9 to 8 before multiplying by 5 in the expression 8(5) + 9, you would get a different result than the correct answer. Following PEMDAS is essential for accurate mathematical calculations.