Problem 9 - Algebra 2

Question

Evaluate each expression if \(w=6, x=0.4, y=\frac{1}{2},\) and \(z=-3\). \(w+x+z\)

Step-by-Step Solution

Answer

The value of the expression is 3.4.

Step 1: Substitute the Values

Substitute the given values of the variables into the expression. The original expression is \(w + x + z\). After substitution, it becomes \(6 + 0.4 + (-3)\).

Step 2: Perform Addition and Subtraction

Perform the addition and subtraction operations in the expression. First, add \(6\) and \(0.4\) to get \(6.4\). Then, add \(-3\) to \(6.4\), resulting in \(6.4 - 3 = 3.4\).

Key Concepts

Substitution

Substitution is an essential concept in evaluating expressions. It involves replacing variables in an expression with their corresponding values. Imagine variables as placeholders that represent specific numbers. When you apply substitution, you swap out the placeholder with its actual value.
For the expression given in the exercise, the variables are replaced with the values:

• For variable \(w\), substitute with 6.
• For variable \(x\), substitute with 0.4.
• For variable \(z\), substitute with -3.

So, the expression \(w + x + z\) becomes \(6 + 0.4 + (-3)\). This step is crucial because it turns a symbolic expression into a numerical one, allowing for further operations like addition and subtraction.

Addition and Subtraction

Once all variables have been substituted with their respective values, the next step involves performing the calculations. Addition and subtraction are basic arithmetic operations and follow the left-to-right rule, meaning you evaluate them in the order they appear from left to right if there are no parentheses guiding the order.
Let's dissect this process with our example:

• Start with the leftmost operation: Add 6 and 0.4. This results in 6.4.
• Next, take the result (6.4) and add \(-3\), the next term in the expression. Subtracting 3 from 6.4 gives you 3.4.

Note how the negative sign in the last term influences the operation: it translates the addition operation into a subtraction of 3. Understanding this will ensure you're performing arithmetic correctly in any expression.

Variable Evaluation

Variable evaluation completes the process of breaking down an expression into a concrete numerical result. What does it entail? It involves not just substituting and performing arithmetic operations, but also interpreting the resulting value in the context of the given expression.
In the exercise, the last expression obtained was 3.4. This is the evaluated value of the original expression \(w + x + z\) given the specific values of \(w = 6\), \(x = 0.4\), and \(z = -3\).
When conducting variable evaluation:

• Check that all variables have been correctly replaced with values before you begin arithmetic operations.
• Ensure each arithmetic step logically follows from the previous one.
• Finally, make sure the evaluated result aligns with the steps performed.

Accurate variable evaluation pairs understanding of the expression's nature with precision in arithmetic calculation, leading to the right result.