Problem 44 - Algebra 1

Question

Evaluate the expression for the given value of the variable. (Review 1.3 and 2.5 for 4.2 ) $$4.2 t+17.9 \text { when } t=3$$

Step-by-Step Solution

Answer

The result of the given expression when \(t = 3\) is \(30.5\).

Step 1: Substitution

Substitute the given value of 't' into the expression. Instead of 't', write '3'. So the expression becomes \(4.2*3 + 17.9\).

Step 2: Perform the multiplication

Now perform the multiplication operation. This means multiplying \(4.2\) by \(3\) which gives \(12.6\). So, the expression now becomes \(12.6 + 17.9\).

Step 3: Addition

The final step is to perform the addition of the two numbers. So, \(12.6 + 17.9\) equals to \(30.5\). This is the final result.

Key Concepts

Substitution

Substitution is the first step when you are asked to evaluate an expression for a given value. Imagine you have a pot with different ingredients, and you decide to replace an ingredient with a new one; similarly, substitution in math involves replacing a variable with a given number.
For the expression provided in the exercise, you are given the variable 't' and you need to replace it with the value 3. This transforms your expression from one with a variable to one that contains only numbers, turning the unknown into a solvable expression:

• Original Expression: \(4.2t + 17.9\)
• Substituted Expression: \(4.2 imes 3 + 17.9\)

By understanding and applying substitution, you unravel the expression to reveal only numbers, making the next steps possible.

Multiplication

After substitution, the next step involves solving the expression through multiplication. Multiplication is a quick way to add a number to itself a specific number of times. In this exercise, you see multiplication between 4.2 and 3:

• Multiplication Expression: \(4.2 imes 3\)
• Result of Multiplication: 12.6

Essentially, you are adding 4.2 three times (4.2 + 4.2 + 4.2) to get 12.6.
This process is essential to breaking down the expression because, without solving the multiplication first, you can't proceed to add the results together effectively.

Addition

With substitution and multiplication completed, your expression should now be simple enough to perform the final operation: addition. Addition is the process of combining numbers to find a total. For this exercise, after you have the multiplication result, you combine it with another number:

• Expression: \(12.6 + 17.9\)

Add these two numbers together to get the final total of 30.5.
By following these steps, you solve the exercise effectively and understand the roles of substitution, multiplication, and addition in evaluating expressions. The steps may seem small on their own, but together they lead to a clear and correct solution.
Each step builds upon the last, showing the importance of following the right order of operations.