Problem 48 - Prealgebra

Question

Find the value of each of the following expressions when \(x = 5\). $$8 x-9$$

Step-by-Step Solution

Answer

The value is 31.

Step 1: Identify the Expression

The expression given is \(8x - 9\). This expression needs evaluation for a specific value of \(x\), which in this case is 5.

Step 2: Substitute the Value of x

Replace the variable \(x\) in the expression with the number 5. This changes the expression from \(8x - 9\) to \(8(5) - 9\).

Step 3: Perform Multiplication

Calculate \(8 \times 5\) to find the product, which is 40. The expression now becomes 40 - 9.

Step 4: Perform Subtraction

Subtract 9 from 40 to get the final result. Therefore, the expression \(40 - 9\) simplifies to 31.

Key Concepts

Variable Substitution

Variable substitution is a fundamental concept in algebra that involves replacing a variable, such as \(x\), with a specific number. This allows us to evaluate expressions and find out their numerical values. When you are given an algebraic expression like \(8x - 9\) and a value for \(x\), you follow these straightforward steps:

• Identify the variable in the expression. In this case, it is \(x\).
• Replace \(x\) with its given number, in this exercise \(x = 5\).
• This changes your expression from \(8x - 9\) to \(8(5) - 9\). This is because anywhere you see \(x\), you substitute it with 5.

By substituting, you've turned a general expression into a specific arithmetic problem that can be further simplified.

Order of Operations

The order of operations is a crucial rule to follow when solving mathematical expressions. It dictates the sequence in which different parts of an expression are computed, ensuring consistent and correct results.
Here's the brief order you should always remember:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Using the acronym PEMDAS (or BIDMAS in some regions), you can determine that multiplication should be done before subtraction when evaluating \(8(5) - 9\). So, you would first calculate \(8 \times 5 = 40\), and then subtract 9, following the proper order for accurate results.

Basic Arithmetic Operations

Understanding basic arithmetic operations is essential for evaluating expressions. These operations include addition, subtraction, multiplication, and division.
For the expression \(8(5) - 9\), we use:

• Multiplication: Here, \(8\) is multiplied by \(5\), resulting in \(40\). Multiplication combines numbers to get a total when you have repeated additions, in this case, adding \(8\) five times.
• Subtraction: After finding the product of the multiplication, you'll perform subtraction in our given expression. Subtract \(9\) from \(40\), which simplifies to \(31\).

Such basic operations are the building blocks of more complex mathematical procedures. Mastery of these ensures success in evaluating almost any expression you encounter.