Problem 58 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable(s). $$49-4 w when w=2$$

Step-by-Step Solution

Answer

The evaluated expression for \(w=2\) is 41.

Step 1: Substitute the value into the expression

Replace 'w' in our expression \(49 - 4w\) with the given value \(2\). So the expression \(49 - 4w\) becomes \(49 - 4 * 2\).

Step 2: Simplify the expression

Perform the multiplication operation before the subtraction as per the BODMAS rule (Brackets, Orders, Division and Multiplication, Addition and Subtraction). So \(49 - 4*2\) simplifies to \(49 - 8\).

Step 3: Perform the subtraction

Subtract 8 from 49 to get the final result, which is 41.

Key Concepts

Substitution

When working with expressions, substitution is an important step. It's the process of replacing a variable with its given value. This helps in transforming a variable expression into a numerical one, which can then be easily calculated. For instance, in the expression \(49 - 4w\) where \(w = 2\), substitution allows us to rewrite the expression as \(49 - 4 \times 2\).

Why is substitution important?

• It helps to simplify complex expressions.
• It gives us concrete numbers to work with, making calculations straightforward.

By using substitution, you're essentially preparing the expression for the next stages of evaluation.

BODMAS Rule

The BODMAS rule is a critical guideline in mathematics that determines the order in which operations should be carried out in an expression. BODMAS stands for:

• Brackets
• Orders (i.e., powers and roots, etc.)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

This order is vital because it ensures that calculations are done correctly and consistently. For example, in the expression \(49 - 4 \times 2\), according to the BODMAS rule, we first perform the multiplication \(4 \times 2 = 8\) before carrying out the subtraction. Ignoring the BODMAS rule can lead to incorrect results, so it's always important to remember it when evaluating expressions.

Simplifying Expressions

Simplifying an expression makes it easier to handle and reduces it to its most straightforward form. This involves carrying out all possible operations defined by the BODMAS rule. For example, after substituting \(w = 2\) into the expression \(49 - 4w\), we obtain \(49 - 8\) after the multiplication.

Here's why simplifying expressions is helpful:

• It reduces complicated problems to simpler forms that are easier to solve.
• It eliminates unnecessary components and focuses on the basic operations to perform.

So, once we reach the simpler expression \(49 - 8\), we only have to perform the single operation of subtraction to get the final result of 41.