Problem 46 - Prealgebra

Question

Find the value of each of the following expressions when \(x = 5\). $$3 x+2$$

Step-by-Step Solution

Answer

When \( x = 5 \), the expression evaluates to 17.

Step 1: Substitute the Value of x

First, we will replace the variable \( x \) in the expression with the given value. The expression is \( 3x + 2 \), and since \( x = 5 \), we substitute 5 for \( x \) to get \( 3(5) + 2 \).

Step 2: Multiply

Next, we need to multiply \( 3 \) by \( 5 \). This gives us \( 15 \). Our expression now looks like \( 15 + 2 \).

Step 3: Add the Numbers

Finally, we add \( 15 \) and \( 2 \) together. This results in \( 17 \). Therefore, the value of the expression when \( x = 5 \) is \( 17 \).

Key Concepts

Variable Substitution

When working with algebraic expressions, a variable such as \( x \) represents a number that can change or that is currently unknown. In our example, we know that this variable represents the number 5.

• To perform variable substitution, simply replace the variable with the number it stands for within the expression.
• If the expression is \( 3x + 2 \) and \( x = 5 \), substitution leads us to \( 3(5) + 2 \).

Variable substitution is a crucial initial step in solving or simplifying algebraic expressions. It allows us to transform abstract expressions into specific numerical operations. This makes it easier to eventually reach a solution.

Evaluating Expressions

Once the variables in an algebraic expression have been replaced with their numerical values, the next step is evaluating the expression, which means calculating its value.
First, adhere to mathematical operations priority or the "order of operations":

• Perform any calculations inside parentheses first.
• Next, do any multiplications or divisions from left to right.
• Lastly, perform any additions or subtractions from left to right.

In our expression, \( 3(5) + 2 \):- We first multiply 3 by 5, which gives 15.- Then, we add 2 to 15, resulting in 17.
Evaluating expressions is a fundamental skill in math. It helps you find the final value of an expression after all operations are performed.

Basic Algebra

Basic algebra is the branch of mathematics that deals with variables and the operations associated with them. It serves as the foundation upon which more complex mathematical concepts are built.
Here are a few key points about basic algebra:

• Algebra involves expressions, which are made up of numbers, variables (like \( x \)), and arithmetic operations.
• It also involves equations, which are statements that two expressions are equal.
• To solve equations or evaluate expressions, substitution is often used to replace variables with known or specified values.

In our example, the expression \( 3x + 2 \) represents a basic algebraic expression. By understanding the concepts and terms of basic algebra, solving and simplifying expressions becomes straightforward. It's a foundational skill you'll use throughout math and science.