Problem 28 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \(9-y\) when \(y=8\)

Step-by-Step Solution

Answer

The result of the expression \(9-y\) when \(y=8\) is 1.

Step 1: Understand the problem

The problem needs to replace the variable \(y\) in the expression \(9-y\) with the given value which is 8. After that, the calculation involves a subtraction operation.

Step 2: Substitute the value

Replace the variable \(y\) in the expression \(9-y\) with the number 8. This makes the equation become \(9-8\).

Step 3: Perform the operation

Perform the subtraction operation. Here, \(9-8\) equals to 1.

Key Concepts

Substitution in Algebra

Substitution in algebra is a fundamental concept where you replace variables within an expression with given values. This technique is used extensively to simplify expressions and solve equations. Imagine you have a letter like "y" in the expression and you're asked to find its value for certain numbers.

Here's how the process works:

• Identify the variable: Determine the letter or symbol that represents an unknown value.
• Find the given value: Check the problem for the number that the variable should be replaced with.
• Replace the variable: Substitute the variable with its corresponding number in the expression.

Once substitution is complete, you convert the expression into a simpler one, ready for further operations. In our problem, we replaced "y" with 8 in the expression \(9-y\). By doing this, we create an expression \(9-8\) which is much simpler to calculate.

Subtraction Operation

Subtraction is a basic mathematical operation that involves finding the difference between two numbers. It tells you how much one number is less than the other.

Consider the subtraction \(9-8\). This involves taking 8 away from 9. You start with the larger number and count back the smaller number. Here, starting from 9:

• Count back 8 places: 9, 8, 7, 6, 5, 4, 3, 2, 1.
• You land on 1, which is the difference.

Thus, the result of the subtraction is 1. Subtraction can also be seen as "finding what's left" after a part is taken away from a whole. Remember, this operation is key to solving many algebraic expressions once variables are substituted with numbers.

Algebraic Expressions

An algebraic expression is a mathematical phrase that includes numbers, variables, and operations. They represent a value or a combination of quantities that can change based on the input.

For example, the expression \(9-y\) is algebraic because it includes:

• A constant number (9).
• A variable (y) representing an unknown value.
• An arithmetic operation (subtraction).

These expressions often allow us to solve problems by plugging in different numbers for the variables, performing the necessary operations, and interpreting the results. In many homework problems, you're asked to evaluate such expressions by performing substitutions. By learning to navigate these components, you gain the skills to solve them accurately and understand their meaning in real-world contexts.