Problem 60 - Algebra A Combined Function

Question

Evaluate each expression when \(x=-5, y=4,\) and \(t=10\). \(y-x\)

Step-by-Step Solution

Answer

The value of the expression is 9.

Step 1: Substitute the values

First, substitute the given values for the variables in the expression: Let \( y = 4 \) and \( x = -5 \). Therefore, the expression becomes: \( 4 - (-5) \).

Step 2: Simplify the expression

Now simplify the expression \( 4 - (-5) \). Subtracting a negative is equivalent to adding, so this becomes \( 4 + 5 \).

Step 3: Compute the result

Finally, add the numbers together: \( 4 + 5 = 9 \).

Key Concepts

Evaluating Expressions

Evaluating expressions involves finding the result of an algebraic expression for given values of the variables. To evaluate an expression like the algebraic expression \(y-x\) for specific values of \(x\) and \(y\), you substitute each variable with its respective value. This allows you to calculate a specific number, providing a concrete answer.
For example, given \(x=-5\) and \(y=4\), substitute these values into the expression to begin simplifying it and arrive at the final outcome.

Substitution Method

The substitution method is a core technique used in algebra to replace variables with their assigned values. This is the first step in evaluating expressions.
When you substitute, you take the values you've been given for each variable and insert them in place of the variable within the expression.

• Let's consider the expression \(y-x\).
• Assign \(y=4\) and \(x=-5\).
• Substitute to transform the expression into \(4 - (-5)\).

Substitution is like swapping placeholders with actual numbers, enabling you to understand the expression better and proceed with simplification.

Simplifying Expressions

Simplifying expressions means making math problems easier to work with by reducing them to their simplest form. Once you've substituted the variables, the next step is to simplify. Start by changing any complex operations to simpler ones.
In our example, you deal with \(4 - (-5)\). Remember, subtracting a negative is the same as adding a positive.

• This complex subtraction is simplified to \(4 + 5\).
• Now that the expression is simple, you're ready to calculate.

Simplification makes expressions more manageable and sets up for finding a straightforward solution.

Integer Operations

Integer operations refer to basic arithmetic operations—addition, subtraction, multiplication, and division—performed on whole numbers. Understanding these helps simplify expressions and compute results.
In the expression \(4 + 5\), we focus on addition:

• Add \(4\) and \(5\) to perform the operation.
• The sum of \(4\) and \(5\) gives \(9\).

Calling back to integer rules is crucial. Addition and subtraction involving negative numbers or subtraction of negatives require special attention to ensure accurate problem-solving.