Problem 42 - Algebra 1: Concepts and Skills

Question

EVALUATING EXPRESSIONS Evaluate the expression for the given value of the variable. \(4.2 t+17.9\) when \(t=3\)

Step-by-Step Solution

Answer

The value of the expression \(4.2t + 17.9\) for \(t = 3\) is \(30.5\).

Step 1: Substitute the given value

Substitute \(t = 3\) into the given expression. The expression now becomes \(4.2 * 3 + 17.9\).

Step 2: Simplify Multiplication

Evaluate \(4.2 * 3\) to get \(12.6\). Our expression now becomes \(12.6 + 17.9\).

Step 3: Simplify Addition

Now evaluate \(12.6 + 17.9\) to get \(30.5\).

Key Concepts

Evaluating Expressions

When we talk about evaluating expressions, we are figuring out what a mathematical expression is equal to. It's like solving a puzzle: replace the variables with given numbers and perform arithmetic to find the answer. In this exercise, you're given the expression \(4.2t + 17.9\) and you're told that \(t = 3\). Your goal is to discover what value this entire expression equals once \(t\) is replaced with the number 3. Evaluating an expression involves:

• Understanding what each symbol and number represents.
• Performing arithmetic operations in the correct sequence, known as the order of operations.

By carefully following these steps, you determine the final value after making the necessary calculations. With practice, evaluating expressions becomes a straightforward process.

Substitution

Substitution in algebra involves replacing a variable with a given number. Picture it as swapping out the letter in an equation with a specific value you are given. In our exercise, this process involves taking the expression \(4.2t + 17.9\) and replacing \(t\) with 3. Here's how substitution breaks down:

• Identify the variable (in this case, \(t\)).
• Replace it with the given number (here, 3).

Once you substitute, the expression \(4.2t + 17.9\) changes to \(4.2 \times 3 + 17.9\). This step sets the stage for simplifying the expression and finding the answer. Substitution is essential for evaluating any algebraic expression where you have known values for the variables.

Simplification

Simplification is the process of making a complex expression easier and manageable by performing all possible arithmetic operations. After substituting the variable with its given number, simplification involves carrying out arithmetic operations like multiplication and addition to reach a final result.In our example, once substitution has turned \(4.2t + 17.9\) into \(4.2 \times 3 + 17.9\):- **Multiply**: First evaluate the multiplication, \(4.2 \times 3\), resulting in 12.6.- **Add**: Then add the result to 17.9, giving you 30.5.Simplification not only provides the solution but also reveals how each part of the expression contributes to the final answer. Always ensure you follow the order of operations: multiplication before addition and subtraction, to get accurate results. Through this methodical process, complex algebraic expressions become simple and coherent.