Problem 24 - Beginning and Intermediate Algebra

Question

Evaluate each expression for ( \(\boldsymbol{a}\) ) \(x=4\) and \((\boldsymbol{b}) x=6\). \(3.275 x\)

Step-by-Step Solution

Answer

For \(x=4\), \(3.275x = 13.1\). For \(x=6\), \(3.275x = 19.65\).

Step 1: Identify the given expression

The given expression is \(3.275x\).

Step 1 Title - Evaluate the expression for \(x=4\)

Substitute \(x=4\) into the expression: \(3.275 \times 4\).

Step 3: Calculate the expression for \(x=4\)

Multiply 3.275 by 4: \[ 3.275 \times 4 = 13.1 \]

Step 2 Title - Evaluate the expression for \(x=6\)

Substitute \(x=6\) into the expression: \(3.275 \times 6\).

Step 5: Calculate the expression for \(x=6\)

Multiply 3.275 by 6: \[ 3.275 \times 6 = 19.65 \]

Key Concepts

Substitution

Substitution is one of the fundamental concepts in algebra that helps us find the value of an expression when a variable is given a specific value.
In our exercise, we were asked to evaluate the expression \(3.275x\) for \(x=4\) and \(x=6\).
To substitute, we simply replace the variable \(x\) with the given numbers in the expression:

• For \(x=4\), the expression becomes \(3.275 \times 4\).
• For \(x=6\), the expression becomes \(3.275 \times 6\).

By following this substitution method, we transform the abstract variable into a concrete number, making it easier to calculate.

Multiplication

Multiplication is a key operation we use after substitution to solve our expression. Once we've substituted the variable with a number, the next step is to multiply:

• For \(x=4\), we need to calculate \(3.275 \times 4\).
• For \(x=6\), we solve \(3.275 \times 6\).

Multiplying decimals is straightforward; align the numbers based on place value and multiply as you would with whole numbers. The product's decimal place is determined by the sum of the decimal places in the factors.
In our solutions:

• \(3.275 \times 4 = 13.1\)
• \(3.275 \times 6 = 19.65\)

Thus, using multiplication, we find the exact values of the expressions for the given values of\ \(x\).

Variable Evaluation

Variable evaluation is the process of finding the value of an expression by determining the variable.
In this exercise, we evaluated the expression \(3.275x\) for different values of \(x\).
Here’s a quick summary of the evaluation steps:

• First, recognize the expression to be evaluated is \(3.275x\).
• Next, use the given values to substitute the variables. For example, \(x=4\) and \(x=6\).
• Finally, perform the multiplication step to obtain the evaluated result: \(13.1\) for \(x=4\) and \(19.65\) for \(x=6\).

Understanding variable evaluation helps in simplifying and solving more complex algebraic equations, making it an essential skill in algebra.