Problem 75 - Algebra 1

Question

Evaluate the expression. \(4+3 x\) when \(x=2\)

Step-by-Step Solution

Answer

The evaluated result of the expression \(4+3 \cdot 2\) equals \(10\).

Step 1: Substitution

The first step involves substituting the value of \(x\) into the expression. We replace \(x\) by \(2\) in the expression: \(4 + 3 \cdot 2\).

Step 2: Perform Multiplication

Next, we use the rule of PEMDAS to first perform the multiplication. Therefore, we multiply \(3\) and \(2\) to get \(6\), so the expression then reads: \(4 + 6\).

Step 3: Perform Addition

Finally, we perform the addition operation. We add \(4\) and \(6\) to get \(10\).

Key Concepts

Substitution Method

The substitution method is a fundamental technique in algebra, crucial for evaluating expressions. It involves replacing variables with their given numerical values. For example, consider the expression 4 + 3x. To evaluate this when x=2, we substitute 2 for every instance of x. Here's how the process looks:

Original Expression: 4 + 3x
Substitute x with 2: 4 + 3(2)

This direct replacement is the essence of the substitution method. By applying it, the expression transforms into a simpler numerical one that we can easily solve using basic arithmetic. Accuracy during the substitution phase is key to obtaining the correct final answer.

Order of Operations

Understanding the order of operations is crucial when solving mathematical expressions. It determines the sequence in which we perform arithmetic operations such as addition, subtraction, multiplication, and division. The conventional order is:

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

This hierarchy ensures that expressions are solved uniformly, yielding consistent results. For the expression after substitution, 4 + 3(2), we follow these rules. We start by handling any operations inside parentheses, then multiplication or division before we move on to addition or subtraction, thus ensuring we always arrive at the correct answer.

PEMDAS

PEMDAS is an acronym that helps students remember the order of operations: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. This principle aligns with the order of operations and is essential when working through mathematical problems.

Applying PEMDAS to our example, 4 + 3(2), we first deal with multiplication before addition. The expression simplifies to 4 + 6. Then, following PEMDAS, we add the numbers to get the final result. Through the PEMDAS guideline, we can systematically approach any expression, reducing errors and ensuring that the calculation process is smooth and accurate.