Problem 94 - Algebra 1

Question

Evaluate the expression for the given value(s) of the variable(s). \(5 x+3\) when \(x=2\)

Step-by-Step Solution

Answer

The value of the expression \(5x + 3\) when \(x = 2\) is 13.

Step 1: Identify the given expression and the value of the variable

The given algebraic expression is \(5x + 3\) and we are asked to find its value when \(x = 2\).

Step 2: Substitute the value of x into the expression

Now, substitute \(x = 2\) into the expression to get: \(5*2 + 3\)

Step 3: Perform Operations

According to the order of operations, we perform multiplication before addition. So, multiply 5 by 2 to get 10 and then add 3 to the result. So, \(5*2 + 3 = 10 + 3\)

Step 4: Complete the Evaluation

Now, adding 10 and 3 gives 13. So, the value of the expression \(5x + 3\) when \(x = 2\) is 13

Key Concepts

Substitution Method

Understanding the substitution method is crucial for evaluating algebraic expressions. It's a technique that involves replacing the variable in an expression with its numerical value. It's akin to substituting ingredients in a recipe; use what's given to find out what the final product is.

For example, consider the expression \(5x + 3\). When we’re told that \(x = 2\), we 'plug in' the value of 2 in place of \(x\). This process transforms our expression into one that only involves numbers, making it straightforward to calculate.

• Start with the original expression: \(5x + 3\).
• Replace the variable \(x\) with its given value: \(5(2) + 3\).
• Simplify the resulting numeric expression to get the answer.

This method not only simplifies the evaluation process but also minimizes errors by providing a clear, step-by-step approach. For further clarity, one might say 'wherever you see \(x\), replace it with 2,' making it easier for learners to track their substitutions.

Order of Operations

The order of operations is an essential set of rules to follow when simplifying mathematical expressions. It's often encapsulated in the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

In the expression \(5*2 + 3\), we follow these steps:

• Multiplication comes before addition, so calculate \(5*2\) first.
• Then, add the result to 3.

Learners often remember the concept with the phrase 'Please Excuse My Dear Aunt Sally.' This rule is vital to get accurate results, as changing the order can lead to completely different answers. It's one of the keystones of arithmetic and algebra, ensuring consistency across calculations.

Variable Evaluation

The process of variable evaluation is about finding the value of an expression with variables once those variables are given specific values. It combines the use of the substitution method and understanding of the order of operations to arrive at a numerical answer.

• Become familiar with the expression and identify all variables.
• Replace each variable with its corresponding value (substitution).
• Apply the order of operations to simplify the expression.

In our example with the expression \(5x + 3\) and \(x = 2\), we've substituted 2 for x and then followed the order of operations to get the final answer, 13. Students should practice this process with different values and types of expressions to become proficient in variable evaluation, an indispensable skill in algebra.